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Other Assets - Summary of Taxable MRBs and GILs Acquired (Parenthetical) (Details) $ in Millions	Sep. 30, 2024 USD ($)
Governmental Issuer Loans [Line Items]
Floor rate	3.95%
Mortgage Revenue Bonds [Member]
Governmental Issuer Loans [Line Items]
Borrower re-allocated previously provided funding	$ 11.5

X

- Definition

Borrower re-allocated previously provided funding.

+ References

No definition available.

+ Details

Name:	ghi_BorrowerReAllocatedPreviouslyProvidedFunding
Namespace Prefix:	ghi_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Governmental issuer loans.

+ References

No definition available.

+ Details

Name:	ghi_GovernmentalIssuerLoansLineItems
Namespace Prefix:	ghi_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Loan Financing Basis Spread on Variable Floor Rate.

+ References

No definition available.

+ Details

Name:	ghi_LoanFinancingBasisSpreadOnVariableFloorRate
Namespace Prefix:	ghi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

X

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=ghi_MortgageRevenueBondsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: