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Fair Value of Financial Instruments - Additional Information (Details) - Fair Value, Inputs, Level 3 [Member] - USD ($) $ in Millions | Sep. 30, 2024 | Dec. 31, 2023
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Governmental Issuer Loan [Member] |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 207.9 | $ 225.7
Taxable Governmental Issuer Loan [Member] |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Available for Sale Security and Property Loan Receivable, Maximum Exposure | $ 2.8 | $ 12.1

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- Definition Available for Sale Security and Property Loan Receivable, Maximum Exposure - This represents the maximum exposure to loss related to the Available for Sale Securities and Property Loan Receivables. + References No definition available. + Details
Name: | ghi_AvailableForSaleSecurityAndPropertyLoanReceivableMaximumExposure
Namespace Prefix: | ghi_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Details
Name: | us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_DebtInstrumentAxis=ghi_GovernmentalIssuerLoanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

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- Details
Name: | us-gaap_DebtInstrumentAxis=ghi_TaxableGovernmentalIssuerLoanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |