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Subsequent Events - Summary of Terms of Interest Rate Swap Agreement (Details) - USD ($)	1 Months Ended	6 Months Ended	12 Months Ended
	Jul. 31, 2023	Jun. 30, 2023	Dec. 31, 2022
Subsequent Event [Line Items]
Derivative, Notional Amount		$ 255,820,231	$ 194,656,088
Mizuho Capital Markets [Member]
Subsequent Event [Line Items]
Derivative Trade Date		2022-12	2022-12
Derivative, Notional Amount		$ 102,489,657	$ 102,690,670
Mizuho Capital Markets [Member] | Subsequent Event [Member]
Subsequent Event [Line Items]
Derivative Trade Date	2023-07
Derivative, Notional Amount	$ 6,240,000
Derivative, Effective Date	Aug. 01, 2023
Derivative, Termination Date	Jun. 01, 2030
Derivative, Fixed Rate Paid	3.645%
Derivative, Variable Rate Index Received	Compounded SOFR
Derivative, Variable Debt Financing Hedged	TOB Trusts

X

- Definition

Derivative effective date 1

+ References

No definition available.

+ Details

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Namespace Prefix:	ghi_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Derivative fixed interest rate paid.

+ References

No definition available.

+ Details

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Balance Type:	na
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X

- Definition

Derivative termination date 1.

+ References

No definition available.

+ Details

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Namespace Prefix:	ghi_
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Balance Type:	na
Period Type:	duration

X

- Definition

Derivative trade date.

+ References

No definition available.

+ Details

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Namespace Prefix:	ghi_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Derivative type of certificates

+ References

No definition available.

+ Details

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

X

- Definition

Derivative variable rate index received.

+ References

No definition available.

+ Details

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

X

- Definition

Nominal or face amount used to calculate payments on the derivative liability.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 1A
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=125515794&loc=SL5579245-113959

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 1B
-URI https://asc.fasb.org/extlink&oid=125515794&loc=SL5580258-113959

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 1A
-Subparagraph (d)
-URI https://asc.fasb.org/extlink&oid=125515794&loc=SL5579245-113959

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event.

+ References

No definition available.

+ Details

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X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
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X

- Details

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
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Period Type: