your employer did it right. they owe you the withholding.
reporting the same wages as the original is correct.
what you have to do is as follows which means taking a deduction or credit in the year of repayment following IRS publication 525 instructions. It deals with repayments under internal code section 1341
Repayments
If you had to repay an amount that you included
in your income in an earlier year, you may be
able to deduct the amount repaid from your income for the year in which you repaid it. Or, if
the amount you repaid is more than $3,000, you
may be able to take a credit against your tax for
the year in which you repaid it. In most cases,
you can claim a deduction or credit only if the
repayment qualifies as an expense or loss incurred in your trade or business or in a for-profit
transaction.
Type of deduction. The type of deduction
you're allowed in the year of repayment depends on the type of income you included in the
earlier year. In most cases, you deduct the repayment on the same form or schedule on
which you previously reported it as income. If you reported it as
wages, unemployment compensation, or other
nonbusiness income, you may be able to deduct it as an other itemized deduction if the
amount repaid is over $3,000.
