Recovery of taxes paid from signing bonus

Hello -

I am trying to work through a unique situation regarding our taxes that I have not dealt with before.

In October 2020 my wife received a signing bonus from a new job she took. While my wife would ultimately be a W2 employee, the signing bonus was not tracked as income and instead was considered a 1099 if I recall.

Fast forward. My wife started a different job in September 2022. Given the stipulations around the signing bonus (if I recall a 3 year commitment), she had to pay back 2/3 of the signing bonus, done via personal check.

I am trying to determine how this is handled from a tax standpoint. Are we able to request a credit back for the taxes we paid on the 2/3 of the signing bonus that we returned to the employer? I've read about it being a deductible amount, but this doesn't appear to help us I assume because we are using the standard deduction.

Thank you very much!