You have articulated it as I understand it. 

The Game and Fish apparently went through an audit sometime after she left employment, and this discrepancy in pay was discovered. So they generated a bill to her for the "overpayment of wages", which she dealt with.  Since, according to them, they could not just void/delete the invoice, they decided to pay her for the amount of the invoice and have her make repayment to close out the invoice.  Now she has received a W2 for the amount of the "repayment".