@kuma_tw
If you use the itemized deduction method on your federal (and possibly state) income tax returns, you don't send any other proof, but keep any documents related to the bonus and repayment for at least 3 years after you file (including emails that say we don't answer emails, or whatever they sent).
For social security on form 843, the instructions say to attach a statement from the employer, and copies of relevant W-2s, and if you can't get a statement from the employer, to attach your own statement detailing why you should get a refund, and that includes your description of efforts to get a statement from your employer and that they refused. In addition to the W-2 showing amounts originally withheld, I would include copies of documents related to the repayment. Not your entire employment contract probably, but at least a statement or receipt or demand letter from the employer and a copy of the canceled check.
