In most cases you do not get a refund of the exact amount of tax that you paid on the overpayment, but you will get an adjustment on your tax return for the year that you pay it back. You do not amend your tax return for the year that you received the overpayment.
The repayment will be shown in box 4 of your SSA-1099 for the year that you pay it back. If you pay it back in 2022, the repayment will be shown on your SSA-1099 for 2022, and it will reduce the net benefits in box 5 that you report on your 2022 tax return. That will reduce the amount of tax that you pay, or increase your refund, on your 2022 tax return. That's how you are compensated for the tax that you paid in the earlier year.
(There is a special way of handling it if the amount you have to pay back in 2022 is more than your benefits for 2022, but that is unlikely in your situation.)
