Relocation allowance

I was paid a relocation allowance by my company in 2021 to move from New York to Louisiana. I received this in two installments of roughly $7,000 each, one before the move and one after (so it was taxed half in NY and half in LA). I signed an agreement that I would repay if I left the company within two years. I was there just over a year before leaving in June 2022.

I received a bill to repay in September 2022for a total of $23k (the total "tax topped" amount of the relocation allowance). I repaid it. I would like to get the roughly $9k that I overpaid on my 2021 taxes back. My question has two parts:

 

1. Do I have to file an amended return for 2021, or since I repaid this in 2022, would it be a reduction in my taxable income for 2022?

2. How do I file this and what supporting documentation is required? I have the paperwork showing the billing I got from my company that I had to repay, but do I need a new W2 from my company or what?

 

Thank you.