Answer:
ยง1002.5(b) states:
Limitation on information about race, color, religion, national origin, or sex. A creditor shall not inquire about the race, color, religion, national origin, or sex of an applicant or any other person in connection with a credit transaction, except as provided in paragraphs (b)(1) and (b)(2) of this section.
It doesn't matter that the loan is closed, this section prohibits you from inquiring about GMI. There are a few exceptions (self-testing and how to title the person).