TurboTax generated a deferral of the employer portion of my self-employed social security taxes in 2020, as it should. I received two notices about payment of the deferred amount from IRS, one addressed to me and one to my wife. I paid them both in 2022. Then, in early 2023, I received a check from IRS for one of those payments. It was labeled "Tax Refund".
Should I claim that extra payment in my 2020 tax return to account for the "Tax Refund" they will say they paid me in 2023?
No, you may not have to report this as income and definitely not by amending your 2020 tax return.
If you claimed the payments as a business expense on your 2022 tax return, you need to report the refund as "Other income - taxable recovery" on your 2023 tax return.
If you didn't claim the payments as a business expense, you don't need to report the refund.
For your future reference, if you filed a joint return the IRS will always send a copy of the letter to both spouses. If it happens again, just pay one of them.