Will my repayment of wage overpayment from prior year be reflected in my W-2?

Due to a payroll error on the employer's part, I was overpaid last year (2019) for 3 months. The way they are doing is:

  • Having me pay back the gross wages from those 3 months
  • Paid me what I should have earned in those 3 months this year

Since this is over $3k that I am paying back to the employer, I will be taking the Claim of Right credit. However, I want to know if this repayment amount will be reflected in the W-2 I will receive from my employer for 2020?

 

I'm asking because I understand the deduction/credit for repayments is to help recoup the federal taxes I paid last year on the gross wages. However, since I am repaying the gross wages to my employer I am paying back the federal and state income tax that was withheld. In the end, this means I am still "out" the tax that was withheld from my paychecks last year. Am I thinking about this correctly?