Actually, by law, they’re not allowed to ask to see a GC again for reverification if at initial hiring you showed an unexpired GC.
6.0 Completing Supplement B, Reverification and Rehire of Form I-9
Reverification is never required for U.S. citizens or noncitizen nationals. Reverification is also never required when the following documents expire: U.S. passports, U.S. passport cards, Permanent Resident Cards) also known as Green Cards), and List B documents. Other noncitizens may require reverification.
Also here:
7.0 Evidence of Employment Authorization for Certain Categories
7.1 Lawful Permanent Residents (LPR)
You must allow employees to choose which document(s) they will present from the Lists of Acceptable Documents. In Section 2, an LPR may choose to present a List A document (such as Form I-551, Permanent Resident Card, commonly referred to as a Green Card) or a List B and C document combination (such as a state-issued driver’s license and unrestricted Social Security card). You are not required to reverify the employment eligibility of a lawful permanent resident who presented these documents and you should not reverify their employment authorization.
Forms I-551 may have:
No expiration date. We issued these cards from January 1977 to August 1989.
A 10-year expiration date.
A two-year expiration date.
Reverification is never required when any of the documents listed above in this section expire.
……
Do not reverify the following documents after they expire:
U.S. passports;
U.S. passport cards;
Form I-551, Alien Registration/Permanent Resident Cards; and
List B documents.
11.4 Avoiding Discrimination in Recruiting, Hiring, and the Form I-9 Process
You should treat people equally when verifying employment authorization and identity.
For example:
Don’t request that someone who presented an unexpired Permanent Resident Card present a new document when the Permanent Resident Card expires.
https://www.uscis.gov/book/export/html/59502