(1) I doubt whether your employer will reissue a 2019 W-2 to correct a payment made in March of 2020.
(2) If you file your tax return now with a balance due, final payment is not required until April 15.
However, I suspect you will be eligible for a right of claim credit or deduction on your 2020 Federal tax return. If so, amending the 2019 tax return will not be required.
See whether this sounds like what you will be repaying in March of 2020.
IRS publication 525 pages 34 and 35 under Repayments.
See also this TurboTax help.
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