Deductions & credits

So, I today I received two W2Cs for 2018 and 2019 from my employer with a boxes 1 through 6 corrected.

First installment of the sign on bonus, $31200, was paid to me in 2018.  On the W2C for 2018 they reduced the wages by $50,000.

Second installment of the bonus $15600 was made in 2019 wholly into a 401k.  On the 2019 W2C they increased my wages by $15600, even though it was made into a pretax 401k plan.

 

 

Repayment of $27,660 was made back to the employer in 2020. I was about 27 % vested into the sign on bonus as per contract.

 

I can't understand the math here as to why they would reduce the 2018 W2C by $50k and increase the 2019 W2C by $15600 even though I had contributed all of the $15600 to a 403b plan.

 

Also,do I need to amend 2018 and 2019 returns as they have issued a W2C for those two years or simply claiming an itemized deduction for 2020 taxes would suffice?