<?xml version="1.0" encoding="US-ASCII"?>
<!-- Generated by Broadridge Transform (tm) - http://www.broadridge.com -->
<!-- Created: Wed Sep 09 14:12:13 UTC 2026 -->
<linkbase xmlns="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ConsolidatedBalanceSheet" roleURI="http://thebankofgreenecounty.com/role/ConsolidatedBalanceSheet"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ConsolidatedIncomeStatement" roleURI="http://thebankofgreenecounty.com/role/ConsolidatedIncomeStatement"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ConsolidatedComprehensiveIncome" roleURI="http://thebankofgreenecounty.com/role/ConsolidatedComprehensiveIncome"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ConsolidatedCashFlow" roleURI="http://thebankofgreenecounty.com/role/ConsolidatedCashFlow"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AmortizedCostandFairValueofSecuritiesAvailableforSaleTable" roleURI="http://thebankofgreenecounty.com/role/AmortizedCostandFairValueofSecuritiesAvailableforSaleTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AmortizedCostandFairValueandAllowanceforCreditLossonSecuritiesHeldtoMaturityTable" roleURI="http://thebankofgreenecounty.com/role/AmortizedCostandFairValueandAllowanceforCreditLossonSecuritiesHeldtoMaturityTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_SecuritiesinContinuousUnrealizedLossPositionTable" roleURI="http://thebankofgreenecounty.com/role/SecuritiesinContinuousUnrealizedLossPositionTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_InvestmentsClassifiedbyContractualMaturityDateTable" roleURI="http://thebankofgreenecounty.com/role/InvestmentsClassifiedbyContractualMaturityDateTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_MajorLoanSegmentsandClassesTable" roleURI="http://thebankofgreenecounty.com/role/MajorLoanSegmentsandClassesTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_LoanBalancesbyInternalCreditQualityIndicatorTable" roleURI="http://thebankofgreenecounty.com/role/LoanBalancesbyInternalCreditQualityIndicatorTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_MajorClassificationsofDepositsTable" roleURI="http://thebankofgreenecounty.com/role/MajorClassificationsofDepositsTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_DepositsbyTimeRemainingonMaturityTable" roleURI="http://thebankofgreenecounty.com/role/DepositsbyTimeRemainingonMaturityTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_DepositsbyTimeRemainingonMaturityTableAlt1" roleURI="http://thebankofgreenecounty.com/role/DepositsbyTimeRemainingonMaturityTableAlt1"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ScheduledMaturitiesofCertificatesofDepositTable" roleURI="http://thebankofgreenecounty.com/role/ScheduledMaturitiesofCertificatesofDepositTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AccumulatedOtherComprehensiveLossTable" roleURI="http://thebankofgreenecounty.com/role/AccumulatedOtherComprehensiveLossTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ComponentsofNetPeriodicPensionCostsTable" roleURI="http://thebankofgreenecounty.com/role/ComponentsofNetPeriodicPensionCostsTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AmountsRecognizedinOtherComprehensiveIncomeTable" roleURI="http://thebankofgreenecounty.com/role/AmountsRecognizedinOtherComprehensiveIncomeTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ProvisionforIncomeTaxesTable" roleURI="http://thebankofgreenecounty.com/role/ProvisionforIncomeTaxesTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_ReconcilestheStatutoryFederalIncomeTaxRatetotheEffectiveIncomeTaxRateTable" roleURI="http://thebankofgreenecounty.com/role/ReconcilestheStatutoryFederalIncomeTaxRatetotheEffectiveIncomeTaxRateTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_DeferredTaxAssetsandLiabilitiesTable" roleURI="http://thebankofgreenecounty.com/role/DeferredTaxAssetsandLiabilitiesTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_SolarTaxCreditInvestmentsandRelatedUnfundedCommitmentsTable" roleURI="http://thebankofgreenecounty.com/role/SolarTaxCreditInvestmentsandRelatedUnfundedCommitmentsTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_NotionalAmountandFairValuesofInterestRateDerivativePositionsTable" roleURI="http://thebankofgreenecounty.com/role/NotionalAmountandFairValuesofInterestRateDerivativePositionsTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_NotionalAmountandFairValuesofInterestRateDerivativePositionsTableAlt1" roleURI="http://thebankofgreenecounty.com/role/NotionalAmountandFairValuesofInterestRateDerivativePositionsTableAlt1"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_UndiscountedCashFlowsofOperatingLeaseLiabilitiesTable" roleURI="http://thebankofgreenecounty.com/role/UndiscountedCashFlowsofOperatingLeaseLiabilitiesTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_UndiscountedCashFlowsofOperatingLeaseLiabilitiesTableAlt1" roleURI="http://thebankofgreenecounty.com/role/UndiscountedCashFlowsofOperatingLeaseLiabilitiesTableAlt1"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AssetsMeasuredatFairValueonRecurringBasisTable" roleURI="http://thebankofgreenecounty.com/role/AssetsMeasuredatFairValueonRecurringBasisTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AssetsMeasuredatFairValueonRecurringBasisTableAlt1" roleURI="http://thebankofgreenecounty.com/role/AssetsMeasuredatFairValueonRecurringBasisTableAlt1"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_CondensedStatementsofFinancialConditionTable" roleURI="http://thebankofgreenecounty.com/role/CondensedStatementsofFinancialConditionTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_CondensedStatementsofIncomeTable" roleURI="http://thebankofgreenecounty.com/role/CondensedStatementsofIncomeTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_CondensedStatementsofCashFlowsTable" roleURI="http://thebankofgreenecounty.com/role/CondensedStatementsofCashFlowsTable"/>
  <roleRef xlink:type="simple" xlink:href="gcbc-20260630.xsd#gcbc_r_AdditionalCalculations" roleURI="http://thebankofgreenecounty.com/role/AdditionalCalculations"/>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ConsolidatedBalanceSheet" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsAndFederalFundsSold"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndDueFromBanks" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndDueFromBanks"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:to="us-gaap_CashAndDueFromBanks" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDepositsInBanks" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDepositsInBanks"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsAndFederalFundsSold" xlink:to="us-gaap_InterestBearingDepositsInBanks" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NotesReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableNet"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NotesReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableGross"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableNet" xlink:to="us-gaap_NotesReceivableGross" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableNet" xlink:to="us-gaap_FinancingReceivableAllowanceForCreditLosses" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_CashCashEquivalentsAndFederalFundsSold" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CertificatesOfDepositAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CertificatesOfDepositAtCarryingValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_CertificatesOfDepositAtCarryingValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FederalHomeLoanBankStock"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_FederalHomeLoanBankStock" order="6" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_NotesReceivableNet" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PropertyPlantAndEquipmentNet" order="8" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BankOwnedLifeInsurance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BankOwnedLifeInsurance"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_BankOwnedLifeInsurance" order="9" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestReceivable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_InterestReceivable" order="10" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PrepaidExpenseAndOtherAssets" order="11" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Deposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Deposits"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoninterestBearingDepositLiabilitiesDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestBearingDepositLiabilitiesDomestic"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_NoninterestBearingDepositLiabilitiesDomestic" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDepositLiabilitiesDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDepositLiabilitiesDomestic"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDepositLiabilitiesDomestic" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_Deposits" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_FederalHomeLoanBankAdvancesMaturitiesSummaryDueWithinOneYearOfBalanceSheetDate" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FederalHomeLoanBankAdvancesLongTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FederalHomeLoanBankAdvancesLongTerm"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_FederalHomeLoanBankAdvancesLongTerm" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubordinatedDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_SubordinatedDebt" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_PreferredStockValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_CommonStockValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AdditionalPaidInCapital" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TreasuryStockCommonValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_StockholdersEquity" xlink:to="us-gaap_TreasuryStockCommonValue" order="6" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_Liabilities" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquity" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ConsolidatedIncomeStatement" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestAndFeeIncomeLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestAndFeeIncomeLoansAndLeases"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestAndFeeIncomeLoansAndLeases" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestIncomeSecuritiesTaxExempt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeSecuritiesTaxExempt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestIncomeSecuritiesTaxExempt" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestIncomeSecuritiesTaxable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeSecuritiesTaxable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="us-gaap_InterestIncomeSecuritiesTaxable" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_InterestBearingDepositsAndFederalFundsSold" xlink:href="gcbc-20260630.xsd#gcbc_InterestBearingDepositsAndFederalFundsSold"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestAndDividendIncomeOperating" xlink:to="gcbc_InterestBearingDepositsAndFederalFundsSold" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseOperating"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseDeposits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseDeposits" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseBorrowings"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestExpenseOperating" xlink:to="us-gaap_InterestExpenseBorrowings" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestIncomeExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseNet"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseNet" xlink:to="us-gaap_InterestAndDividendIncomeOperating" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseNet" xlink:to="us-gaap_InterestExpenseOperating" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="us-gaap_InterestIncomeExpenseNet" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" xlink:to="us-gaap_ProvisionForLoanLeaseAndOtherLosses" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoninterestIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestIncome"/>
    <loc xlink:type="locator" xlink:label="gcbc_ServiceChargesOnDepositAccounts" xlink:href="gcbc-20260630.xsd#gcbc_ServiceChargesOnDepositAccounts"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="gcbc_ServiceChargesOnDepositAccounts" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebitCardFees" xlink:href="gcbc-20260630.xsd#gcbc_DebitCardFees"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="gcbc_DebitCardFees" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_InvestmentBankingAdvisoryBrokerageAndUnderwritingFeesAndCommissions" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ECommerceFees" xlink:href="gcbc-20260630.xsd#gcbc_ECommerceFees"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="gcbc_ECommerceFees" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BankOwnedLifeInsuranceIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BankOwnedLifeInsuranceIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_BankOwnedLifeInsuranceIncome" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherOperatingIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherOperatingIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestIncome" xlink:to="us-gaap_OtherOperatingIncome" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestExpense"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LaborAndRelatedExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_LaborAndRelatedExpense" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OccupancyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OccupancyNet"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_OccupancyNet" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquipmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquipmentExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_EquipmentExpense" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InformationTechnologyAndDataProcessing" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InformationTechnologyAndDataProcessing"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_InformationTechnologyAndDataProcessing" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ComputerSoftwareSuppliesAndSupport" xlink:href="gcbc-20260630.xsd#gcbc_ComputerSoftwareSuppliesAndSupport"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="gcbc_ComputerSoftwareSuppliesAndSupport" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AdvertisingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdvertisingExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_AdvertisingExpense" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FederalDepositInsuranceCorporationPremiumExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FederalDepositInsuranceCorporationPremiumExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_FederalDepositInsuranceCorporationPremiumExpense" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProfessionalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfessionalFees"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_ProfessionalFees" order="8" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherNoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoninterestExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NoninterestExpense" xlink:to="us-gaap_OtherNoninterestExpense" order="9" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_NoninterestIncome" order="2" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="us-gaap_NoninterestExpense" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_IncomeTaxExpenseBenefit" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ConsolidatedComprehensiveIncome" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossPensionAndOtherPostretirementBenefitPlansNetUnamortizedGainLossArisingDuringPeriodBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeFinalizationOfPensionAndNonPensionPostretirementPlanValuationTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeFinalizationOfPensionAndNonPensionPostretirementPlanValuationTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeFinalizationOfPensionAndNonPensionPostretirementPlanValuationTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" order="2" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossFinalizationOfPensionAndNonPensionPostretirementPlanValuationNetOfTax" order="3" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" order="4" weight="-1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" order="5" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_NetIncomeLoss" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ConsolidatedCashFlow" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetIncomeLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DepreciationNonproduction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationNonproduction"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DepreciationNonproduction" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DeferredIncomeTaxExpenseBenefit" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AmortizationOfFinancingCosts" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProvisionForLoanLeaseAndOtherLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProvisionForLoanLeaseAndOtherLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_ProvisionForLoanLeaseAndOtherLosses" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccruedIncomeTaxesPayable" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" order="8" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfDeferredLoanOriginationFeesNet"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AmortizationOfDeferredLoanOriginationFeesNet" order="9" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_BankOwnedLifeInsuranceIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BankOwnedLifeInsuranceIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_BankOwnedLifeInsuranceIncome" order="10" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" order="11" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquitySecuritiesFvNiGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiGainLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_EquitySecuritiesFvNiGainLoss" order="12" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_GainsLossesOnSalesOfOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnSalesOfOtherRealEstate"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_GainsLossesOnSalesOfOtherRealEstate" order="13" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInInterestAndDividendsReceivable" order="14" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" order="15" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesAvailableForSalePrincipalPaymentsOnSecurities" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesAvailableForSalePrincipalPaymentsOnSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="gcbc_SecuritiesAvailableForSalePrincipalPaymentsOnSecurities" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleAndMaturityOfHeldToMaturitySecurities" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesHeldToMaturitiesPrincipalPaymentsOnSecurities" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesHeldToMaturitiesPrincipalPaymentsOnSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="gcbc_SecuritiesHeldToMaturitiesPrincipalPaymentsOnSecurities" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ProceedsFromMaturitiesOfLongTermCertificatesOfDeposit" xlink:href="gcbc-20260630.xsd#gcbc_ProceedsFromMaturitiesOfLongTermCertificatesOfDeposit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="gcbc_ProceedsFromMaturitiesOfLongTermCertificatesOfDeposit" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromLifeInsurancePolicies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromLifeInsurancePolicies"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromLifeInsurancePolicies" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromSaleOfForeclosedAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfForeclosedAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_ProceedsFromSaleOfForeclosedAssets" order="8" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" order="9" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireHeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireHeldToMaturitySecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireHeldToMaturitySecurities" order="10" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsForProceedsFromFederalHomeLoanBankStock" order="11" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquireLifeInsurancePolicies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireLifeInsurancePolicies"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquireLifeInsurancePolicies" order="12" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForProceedsFromLoansAndLeases" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForProceedsFromLoansAndLeases"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsForProceedsFromLoansAndLeases" order="13" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" order="14" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfLongTermDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_ProceedsFromIssuanceOfLongTermDebt" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInDeposits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_IncreaseDecreaseInDeposits" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ProceedsFromPaymentsOfShortTermFHLBankBorrowingsFinancingActivities" xlink:href="gcbc-20260630.xsd#gcbc_ProceedsFromPaymentsOfShortTermFHLBankBorrowingsFinancingActivities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="gcbc_ProceedsFromPaymentsOfShortTermFHLBankBorrowingsFinancingActivities" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RepaymentsOfOtherLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfOtherLongTermDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_RepaymentsOfOtherLongTermDebt" order="4" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RepaymentsOfSubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSubordinatedDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_RepaymentsOfSubordinatedDebt" order="5" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsForRepurchaseOfCommonStock" order="6" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsOfDividends" order="7" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInInvestingActivities" order="2" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities" order="3" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AmortizedCostandFairValueofSecuritiesAvailableforSaleTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" order="3" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AmortizedCostandFairValueandAllowanceforCreditLossonSecuritiesHeldtoMaturityTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecurities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="us-gaap_HeldToMaturitySecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/SecuritiesinContinuousUnrealizedLossPositionTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebtSecuritiesHeldToMaturityUnrealizedLossPositionsFairValue" xlink:href="gcbc-20260630.xsd#gcbc_DebtSecuritiesHeldToMaturityUnrealizedLossPositionsFairValue"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsFairValue" xlink:href="gcbc-20260630.xsd#gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_DebtSecuritiesHeldToMaturityUnrealizedLossPositionsFairValue" xlink:to="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerFairValue" xlink:href="gcbc-20260630.xsd#gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_DebtSecuritiesHeldToMaturityUnrealizedLossPositionsFairValue" xlink:to="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsAccumulatedLoss" xlink:href="gcbc-20260630.xsd#gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:to="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositionsLessThan12MonthsAccumulatedLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerAccumulatedLoss" xlink:href="gcbc-20260630.xsd#gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:to="gcbc_DebtSecuritiesHeldToMaturityContinuousUnrealizedLossPositions12MonthsOrLongerAccumulatedLoss" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_HeldToMaturitySecuritiesInUnrealizedLossesPositionsQualitativeDisclosureNumberOfSecurityPositions" xlink:href="gcbc-20260630.xsd#gcbc_HeldToMaturitySecuritiesInUnrealizedLossesPositionsQualitativeDisclosureNumberOfSecurityPositions"/>
    <loc xlink:type="locator" xlink:label="gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsLessThanOneYear" xlink:href="gcbc-20260630.xsd#gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsLessThanOneYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_HeldToMaturitySecuritiesInUnrealizedLossesPositionsQualitativeDisclosureNumberOfSecurityPositions" xlink:to="gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsLessThanOneYear" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsGreaterThanOrEqualToOneYear" xlink:href="gcbc-20260630.xsd#gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsGreaterThanOrEqualToOneYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_HeldToMaturitySecuritiesInUnrealizedLossesPositionsQualitativeDisclosureNumberOfSecurityPositions" xlink:to="gcbc_HeldToMaturitySecuritiesInUnrealizedLossPositionsQualitativeDisclosureNumberOfPositionsGreaterThanOrEqualToOneYear" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPositionsFairValue" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPositionsFairValue"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SecuritiesContinuousUnrealizedLossPositionsFairValue" xlink:to="gcbc_SecuritiesContinuousUnrealizedLossPositionLessThanTwelveMonthsFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SecuritiesContinuousUnrealizedLossPositionsFairValue" xlink:to="gcbc_SecuritiesContinuousUnrealizedLossPositionTwelveMonthsOrLongerFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPositionsAccumulatedLoss" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPositionsAccumulatedLoss"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SecuritiesContinuousUnrealizedLossPositionsAccumulatedLoss" xlink:to="gcbc_SecuritiesContinuousUnrealizedLossPositionAccumulatedLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_SecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="gcbc-20260630.xsd#gcbc_SecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SecuritiesContinuousUnrealizedLossPositionsAccumulatedLoss" xlink:to="gcbc_SecuritiesContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_NumberOfSecuritiesUnrealizedLossPosition" xlink:href="gcbc-20260630.xsd#gcbc_NumberOfSecuritiesUnrealizedLossPosition"/>
    <loc xlink:type="locator" xlink:label="gcbc_NumberOfSecuritiesUnrealizedLossPositionLessThanTwelveMonths" xlink:href="gcbc-20260630.xsd#gcbc_NumberOfSecuritiesUnrealizedLossPositionLessThanTwelveMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_NumberOfSecuritiesUnrealizedLossPosition" xlink:to="gcbc_NumberOfSecuritiesUnrealizedLossPositionLessThanTwelveMonths" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_NumberOfSecuritiesUnrealizedLossPositionTwelveMonthsOrLonger" xlink:href="gcbc-20260630.xsd#gcbc_NumberOfSecuritiesUnrealizedLossPositionTwelveMonthsOrLonger"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_NumberOfSecuritiesUnrealizedLossPosition" xlink:to="gcbc_NumberOfSecuritiesUnrealizedLossPositionTwelveMonthsOrLonger" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/InvestmentsClassifiedbyContractualMaturityDateTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateNetCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateNetCarryingAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateNetCarryingAmount" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostBeforeAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostBeforeAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostBeforeAllowanceForCreditLoss" xlink:to="us-gaap_HeldToMaturitySecurities" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostBeforeAllowanceForCreditLoss" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" order="2" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostBeforeAllowanceForCreditLoss" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityFairValue" xlink:to="us-gaap_HeldToMaturitySecuritiesFairValue" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/MajorLoanSegmentsandClassesTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_NotesReceivableNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableNet"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NotesReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableGross"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableNet" xlink:to="us-gaap_NotesReceivableGross" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableNet" xlink:to="us-gaap_FinancingReceivableAllowanceForCreditLosses" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/LoanBalancesbyInternalCreditQualityIndicatorTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_NotesReceivableGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesReceivableGross"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableRevolving" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRevolving"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableRevolving" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoan" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRevolvingConvertedToTermLoan"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NotesReceivableGross" xlink:to="us-gaap_FinancingReceivableRevolvingConvertedToTermLoan" order="8" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableYearOneOriginatedCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableYearOneOriginatedCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableYearOneOriginatedCurrentFiscalYearWriteoff" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableYearTwoOriginatedFiscalYearBeforeCurrentFiscalYearWriteoff" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableRevolvingWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRevolvingWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableRevolvingWriteoff" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoanWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinancingReceivableRevolvingConvertedToTermLoanWriteoff"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs" xlink:to="us-gaap_FinancingReceivableRevolvingConvertedToTermLoanWriteoff" order="8" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/MajorClassificationsofDepositsTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_Deposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Deposits"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NoninterestBearingDepositLiabilitiesDomestic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoninterestBearingDepositLiabilitiesDomestic"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_NoninterestBearingDepositLiabilitiesDomestic" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDomesticDepositCertificatesOfDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDomesticDepositCertificatesOfDeposits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDomesticDepositCertificatesOfDeposits" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDomesticDepositSavings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDomesticDepositSavings"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDomesticDepositSavings" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDomesticDepositMoneyMarket" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDomesticDepositMoneyMarket"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDomesticDepositMoneyMarket" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestBearingDomesticDepositNegotiableOrderOfWithdrawalNOW" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestBearingDomesticDepositNegotiableOrderOfWithdrawalNOW"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Deposits" xlink:to="us-gaap_InterestBearingDomesticDepositNegotiableOrderOfWithdrawalNOW" order="5" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/DepositsbyTimeRemainingonMaturityTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositsLessThan250000" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositsLessThan250000"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsOrLess" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsOrLess"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositsLessThan250000" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsOrLess" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsThroughSixMonths" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsThroughSixMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositsLessThan250000" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsThroughSixMonths" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDepositsLessThan250000SixMonthsThrough12Months" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDepositsLessThan250000SixMonthsThrough12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositsLessThan250000" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000SixMonthsThrough12Months" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDepositsLessThan250000After12Months" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDepositsLessThan250000After12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositsLessThan250000" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000After12Months" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDeposits250000OrMore" xlink:href="gcbc-20260630.xsd#gcbc_TimeDeposits250000OrMore"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsOrLess" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsOrLess"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDeposits250000OrMore" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsOrLess" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsThroughSixMonths" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsThroughSixMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDeposits250000OrMore" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsThroughSixMonths" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDeposits250000OrMore6MonthsThrough12Months" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDeposits250000OrMore6MonthsThrough12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDeposits250000OrMore" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMore6MonthsThrough12Months" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreAfter12Months" xlink:href="gcbc-20260630.xsd#gcbc_ContractualMaturitiesTimeDeposits250000OrMoreAfter12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDeposits250000OrMore" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreAfter12Months" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesThreeMonthsOrLess" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesThreeMonthsOrLess"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesThreeMonthsOrLess" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsOrLess" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesThreeMonthsOrLess" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsOrLess" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000ThreeMonthsThroughSixMonths" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreThreeMonthsThroughSixMonths" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesSixMonthsThrough12Months" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesSixMonthsThrough12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesSixMonthsThrough12Months" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000SixMonthsThrough12Months" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesSixMonthsThrough12Months" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMore6MonthsThrough12Months" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesAfter12Months" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesAfter12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesAfter12Months" xlink:to="gcbc_ContractualMaturitiesTimeDepositsLessThan250000After12Months" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_TimeDepositMaturitiesAfter12Months" xlink:to="gcbc_ContractualMaturitiesTimeDeposits250000OrMoreAfter12Months" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDeposits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDepositsLessThan250000" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDeposits250000OrMore" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/DepositsbyTimeRemainingonMaturityTableAlt1" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDeposits"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesThreeMonthsOrLess" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesThreeMonthsOrLess"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDepositMaturitiesThreeMonthsOrLess" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDepositMaturitiesThreeMonthsThroughSixMonths" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesSixMonthsThrough12Months" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesSixMonthsThrough12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDepositMaturitiesSixMonthsThrough12Months" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_TimeDepositMaturitiesAfter12Months" xlink:href="gcbc-20260630.xsd#gcbc_TimeDepositMaturitiesAfter12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="gcbc_TimeDepositMaturitiesAfter12Months" order="4" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ScheduledMaturitiesofCertificatesofDepositTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDeposits"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDepositMaturitiesYearOne" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDepositMaturitiesYearOne"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearOne" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDepositMaturitiesYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDepositMaturitiesYearTwo"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearTwo" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDepositMaturitiesYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDepositMaturitiesYearThree"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearThree" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDepositMaturitiesYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDepositMaturitiesYearFour"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearFour" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_TimeDepositMaturitiesYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TimeDepositMaturitiesYearFive"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_TimeDeposits" xlink:to="us-gaap_TimeDepositMaturitiesYearFive" order="5" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AccumulatedOtherComprehensiveLossTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossTax" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesNetOfTax" order="2" weight="-1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIPensionAndOtherPostretirementBenefitPlansForNetGainLossNetOfTax" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseNetOfTax" xlink:href="gcbc-20260630.xsd#gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseNetOfTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseNetOfTax" order="4" weight="-1"/>
    <loc xlink:type="locator" xlink:label="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseBeforeTax" xlink:href="gcbc-20260630.xsd#gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseNetOfTax" xlink:to="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseBeforeTax" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseTax" xlink:href="gcbc-20260630.xsd#gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseNetOfTax" xlink:to="gcbc_OtherComprehensiveIncomeLossPensionTerminationSettlementChargeRecognizedInOtherExpenseTax" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ComponentsofNetPeriodicPensionCostsTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanInterestCost" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanInterestCost"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="us-gaap_DefinedBenefitPlanInterestCost" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="us-gaap_DefinedBenefitPlanExpectedReturnOnPlanAssets" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="us-gaap_DefinedBenefitPlanAmortizationOfGainsLosses" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlements1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlements1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DefinedBenefitPlanNetPeriodicBenefitCost" xlink:to="us-gaap_DefinedBenefitPlanRecognizedNetGainLossDueToSettlements1" order="4" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AmountsRecognizedinOtherComprehensiveIncomeTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansAdjustmentNetOfTaxPortionAttributableToParent"/>
    <loc xlink:type="locator" xlink:label="gcbc_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossDeferredTaxExpense" xlink:href="gcbc-20260630.xsd#gcbc_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossDeferredTaxExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="gcbc_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossDeferredTaxExpense" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossNetGainLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossNetGainLossBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="us-gaap_DefinedBenefitPlanAmountsRecognizedInOtherComprehensiveIncomeLossNetGainLossBeforeTax" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ProvisionforIncomeTaxesTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentFederalTaxExpenseBenefit" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CurrentStateAndLocalTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="us-gaap_CurrentStateAndLocalTaxExpenseBenefit" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredFederalIncomeTaxExpenseBenefit" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <loc xlink:type="locator" xlink:label="us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperations"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_FederalIncomeTaxExpenseBenefitContinuingOperations" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StateAndLocalIncomeTaxExpenseBenefitContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StateAndLocalIncomeTaxExpenseBenefitContinuingOperations"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_StateAndLocalIncomeTaxExpenseBenefitContinuingOperations" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/ReconcilestheStatutoryFederalIncomeTaxRatetotheEffectiveIncomeTaxRateTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationOtherAdjustments" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_IncomeTaxReconciliationTaxCreditsNetOfAmortization" xlink:href="gcbc-20260630.xsd#gcbc_IncomeTaxReconciliationTaxCreditsNetOfAmortization"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="gcbc_IncomeTaxReconciliationTaxCreditsNetOfAmortization" order="4" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationTaxExemptIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="us-gaap_IncomeTaxReconciliationTaxExemptIncome" order="5" weight="-1"/>
    <loc xlink:type="locator" xlink:label="gcbc_IncomeTaxReconciliationNondeductibleExpenseLifeInsuranceIncreaseInSurrenderValue" xlink:href="gcbc-20260630.xsd#gcbc_IncomeTaxReconciliationNondeductibleExpenseLifeInsuranceIncreaseInSurrenderValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_IncomeTaxExpenseBenefit" xlink:to="gcbc_IncomeTaxReconciliationNondeductibleExpenseLifeInsuranceIncreaseInSurrenderValue" order="6" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationStateAndLocalIncomeTaxes" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationOtherAdjustments" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_EffectiveIncomeTaxRateReconciliationTaxCreditNetOfAmortization" xlink:href="gcbc-20260630.xsd#gcbc_EffectiveIncomeTaxRateReconciliationTaxCreditNetOfAmortization"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="gcbc_EffectiveIncomeTaxRateReconciliationTaxCreditNetOfAmortization" order="4" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome" order="5" weight="-1"/>
    <loc xlink:type="locator" xlink:label="gcbc_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseIncreaseInSurrenderValueOfBankOwnedLifeInsurance" xlink:href="gcbc-20260630.xsd#gcbc_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseIncreaseInSurrenderValueOfBankOwnedLifeInsurance"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="gcbc_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseIncreaseInSurrenderValueOfBankOwnedLifeInsurance" order="6" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/DeferredTaxAssetsandLiabilitiesTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsGross"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsProvisionForLoanLosses" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DeferredTaxAssetsAllowanceForCreditLossesOnUnfundedCommitments" xlink:href="gcbc-20260630.xsd#gcbc_DeferredTaxAssetsAllowanceForCreditLossesOnUnfundedCommitments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="gcbc_DeferredTaxAssetsAllowanceForCreditLossesOnUnfundedCommitments" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsUnrealizedLossesOnAvailableforSaleSecuritiesGross" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsOther"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsOther" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DeferredTaxAssetsSolarTaxCreditInvestments" xlink:href="gcbc-20260630.xsd#gcbc_DeferredTaxAssetsSolarTaxCreditInvestments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="gcbc_DeferredTaxAssetsSolarTaxCreditInvestments" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DeferredTaxAssetsLeaseLiability" xlink:href="gcbc-20260630.xsd#gcbc_DeferredTaxAssetsLeaseLiability"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="gcbc_DeferredTaxAssetsLeaseLiability" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsOther"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsGross" xlink:to="us-gaap_DeferredTaxAssetsOther" order="7" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DeferredTaxLiabilitiesDeferredLoanCosts" xlink:href="gcbc-20260630.xsd#gcbc_DeferredTaxLiabilitiesDeferredLoanCosts"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="gcbc_DeferredTaxLiabilitiesDeferredLoanCosts" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxLiabilitiesTaxDeferredIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilitiesTaxDeferredIncome"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesTaxDeferredIncome" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilitiesLeasingArrangements"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesLeasingArrangements" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_DeferredTaxLiabilitiesPensionBenefits" xlink:href="gcbc-20260630.xsd#gcbc_DeferredTaxLiabilitiesPensionBenefits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="gcbc_DeferredTaxLiabilitiesPensionBenefits" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredIncomeTaxLiabilities" xlink:to="us-gaap_DeferredTaxLiabilitiesOther" order="6" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredTaxAssetsLiabilitiesNet"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredTaxAssetsGross" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:to="us-gaap_DeferredIncomeTaxLiabilities" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/SolarTaxCreditInvestmentsandRelatedUnfundedCommitmentsTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="gcbc_SolarTaxCreditInvestmentsNet" xlink:href="gcbc-20260630.xsd#gcbc_SolarTaxCreditInvestmentsNet"/>
    <loc xlink:type="locator" xlink:label="gcbc_SolarTaxCreditInvestmentsGross" xlink:href="gcbc-20260630.xsd#gcbc_SolarTaxCreditInvestmentsGross"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SolarTaxCreditInvestmentsNet" xlink:to="gcbc_SolarTaxCreditInvestmentsGross" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="gcbc_AccumulatedAmortizationOnSolarTaxCreditInvestments" xlink:href="gcbc-20260630.xsd#gcbc_AccumulatedAmortizationOnSolarTaxCreditInvestments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="gcbc_SolarTaxCreditInvestmentsNet" xlink:to="gcbc_AccumulatedAmortizationOnSolarTaxCreditInvestments" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/NotionalAmountandFairValuesofInterestRateDerivativePositionsTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeFairValueOfDerivativeAsset" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeCollateralObligationToReturnCash" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeFairValueOfDerivativeLiability" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeCollateralRightToReclaimCash" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/NotionalAmountandFairValuesofInterestRateDerivativePositionsTableAlt1" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeAsset"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeFairValueOfDerivativeAsset" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeCollateralObligationToReturnCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralObligationToReturnCash"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeAssetAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeCollateralObligationToReturnCash" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeFairValueOfDerivativeLiability" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DerivativeCollateralRightToReclaimCash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeCollateralRightToReclaimCash"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountOffsetAgainstCollateral" xlink:to="us-gaap_DerivativeCollateralRightToReclaimCash" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/UndiscountedCashFlowsofOperatingLeaseLiabilitiesTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" order="4" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" order="5" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" order="6" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/UndiscountedCashFlowsofOperatingLeaseLiabilitiesTableAlt1" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiability"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_OperatingLeaseLiability" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AssetsMeasuredatFairValueonRecurringBasisTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateDerivativeAssetsAtFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_InterestRateDerivativeAssetsAtFairValue" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestRateDerivativeLiabilitiesAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateDerivativeLiabilitiesAtFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesFairValueDisclosure" xlink:to="us-gaap_InterestRateDerivativeLiabilitiesAtFairValue" order="1" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AssetsMeasuredatFairValueonRecurringBasisTableAlt1" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestRateDerivativeAssetsAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateDerivativeAssetsAtFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AssetsFairValueDisclosure" xlink:to="us-gaap_InterestRateDerivativeAssetsAtFairValue" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestRateDerivativeLiabilitiesAtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestRateDerivativeLiabilitiesAtFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesFairValueDisclosure" xlink:to="us-gaap_InterestRateDerivativeLiabilitiesAtFairValue" order="1" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/CondensedStatementsofFinancialConditionTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestments"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_EquityMethodInvestments" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PrepaidExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseAndOtherAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Assets" xlink:to="us-gaap_PrepaidExpenseAndOtherAssets" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_SubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubordinatedDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_SubordinatedDebt" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Liabilities" xlink:to="us-gaap_AccruedLiabilitiesAndOtherLiabilities" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_Liabilities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="us-gaap_StockholdersEquity" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/CondensedStatementsofIncomeTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Revenues"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendIncomeOperating"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_DividendIncomeOperating" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestIncomeDomesticDeposits" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestIncomeDomesticDeposits"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_Revenues" xlink:to="us-gaap_InterestIncomeDomesticDeposits" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpenses"/>
    <loc xlink:type="locator" xlink:label="us-gaap_LegalFees" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LegalFees"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_LegalFees" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseBorrowings"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_InterestExpenseBorrowings" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_OtherNoninterestExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoninterestExpense"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_OperatingExpenses" xlink:to="us-gaap_OtherNoninterestExpense" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_Revenues" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetIncomeLoss" xlink:to="us-gaap_OperatingExpenses" order="2" weight="-1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/CondensedStatementsofCashFlowsTable" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_NetIncomeLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_AmortizationOfFinancingCosts" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayable"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInAccountsPayable" order="3" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncomeLossFromEquityMethodInvestmentsNetOfDividendsOrDistributions" order="4" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" order="5" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsOfDividends" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfDividends"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsOfDividends" order="1" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_PaymentsForRepurchaseOfCommonStock" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_RepaymentsOfSubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSubordinatedDebt"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="us-gaap_RepaymentsOfSubordinatedDebt" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInOperatingActivities" order="1" weight="1"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect" xlink:to="us-gaap_NetCashProvidedByUsedInFinancingActivities" order="2" weight="1"/>
  </calculationLink>
  <calculationLink xlink:role="http://thebankofgreenecounty.com/role/AdditionalCalculations" xlink:type="extended">
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleSecuritiesDebtSecurities"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleSecuritiesDebtSecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecurities"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesFairValue"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesFairValue" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingLoss" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_HeldToMaturitySecurities" xlink:to="us-gaap_HeldToMaturitySecuritiesAccumulatedUnrecognizedHoldingGain" order="3" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="us-gaap_HeldToMaturitySecurities" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss" xlink:to="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLoss" order="2" weight="-1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLonger" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss" order="2" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions"/>
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsNumberOfPositions" order="1" weight="1"/>
    <loc xlink:type="locator" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions"/>
<!-- [WMV7][vi9TqWDpd7qPISFG2HQKm4h3NUyoVghTyvY7AhXvg5atdS5HphyYHf+tuVnQCzSEDskpIXt39SC+L8Cx2yMC2kdoqAdRoUa68dv+GkYsmh1PEl0uyxAXu0NGZF4VHdgacrPQN7IR0zH/eFnltuotbV2DL3lAyPFgLfVUZATL3+EJ94RxSE6Bs0MpQrxBbAGSNn5IM1MYy7w7mY1Jn9w6nwnw9ezBqvVk+U2cGTxijc6EfmIUvbqOmGqnXr62hs5eBw2UtjEe3FybZ4HXRB7zF6ryTtUNcKj+PGjBgDpIwRK/IO/rdIQZjbMAXnzAJnmCsjFupegBulSvyQUpRnZoCwk1v/ugqyLpsESsNU9qsOUY] CSR-->
    <calculationArc xlink:type="arc" xlink:arcrole="http://www.xbrl.org/2003/arcrole/summation-item" xlink:from="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions" xlink:to="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerNumberOfPositions" order="2" weight="1"/>
  </calculationLink>
</linkbase>
