Gross relocation repayment - How to get tax refunded?

I was asked by my former company to pay back the gross amount of the relocation payment I received ($14214.63 gross that led to $10000.00 net) which I did. I received the payment in 2021 and paid it back in 2022. I contacted HR at my former company asking if they could send me an adjusted wage form to indicate this. However, I heard back from them saying that the company cannot refund FICA taxes (I suppose this would be the Social Security and Medicare taxes) from a prior year and that I would need to file for any refund with the federal tax authorities. Because of this, they said they couldn't issue me a W2-C. 

 

Does anyone know what the best course of action should be for me from here? How should I go about getting the federal tax refunded? And is there any way to get the FICA tax refunded as well? Note that there was no state income tax involved as the State I was working in does not have one.