Publication 15 shows that an employer needs to amend the 941 for "Wage Repayments". Although it refers to wages paid in "error", it also applies to this type of repayment.
When the employer amends the 941, the employer gets back BOTH halves of Social Security and Medicare taxes. So the employer owes the employee those amounts.
Repayment of prior year wages.
If you receive repayments for wages paid during a prior year, report an adjustment on Form 941-X or Form 944-X to recover the social security and Medicare taxes. You can't make an adjustment for income tax withholding because the wages were income to the employee for the prior year. You can't make an adjustment for Additional Medicare Tax withholding because the employee determines liability for Additional Medicare Tax on the employee's income tax return for the prior year.
You must also file Forms W-2c and W-3c with the SSA to correct social security and Medicare wages and taxes. Don't correct wages (box 1) on Form W-2c for the amount paid in error. Give a copy of Form W-2c to the employee.
https://www.irs.gov/publications/p15#en_US_2020_publink[phone number removed]
