Are postmark dates applicable for repayments as per IRS publication 525?

Imagine I write/mail a check for $5000 as the repayment amount on 12/27/2020.

When does this have to be processed? Is it considered part of 2020's tax year as long as the check is postmarked prior to 1/1/2021? Or is there a requirement that the employer also process the check in 2020?

When you are sending forms/payment to the IRS the postmark is the key. Of course in most cases the IRS is the one with the proof, because they have the envelope. For many people that uncertainty has been reduced by the movement towards electronic filing. In that situation the only issue is did you push the submit button before midnight on the deadline day. The software/service captures the time.

One place this does come up is charitable donations. When made by check it had to be postmarked by midnight on 31 December. I haven't tested the system to know if the charity I donate to looks at the postmark to determine the year. I do know that when they are made by credit card online, then it is the date of when you click submit, and not the date you pay the credit card bill.

Looking specifically at:

When does this have to be processed?

Because when it is processed is out of your control, it can't be dependent on when your employer completes their entire process.

Is it considered part of 2020's tax year as long as the check is postmarked prior to 1/1/2021?

This is more problematic.

If the employer has to assign it to the correct year so that it is properly assigned to the correct W-2 then postmarking it in the last few days of the year is assuming that they will note the date of the postmark when recording the receipt.

My concern comes from this paragraph in pub 525 even though it doesn't at first seem to apply because it has to do with your income:

Constructively received income.

You are generally taxed on income that is available to you, regardless of whether it is actually in your possession.

A valid check that you received or that was made available to you before the end of the tax year is considered income constructively received in that year, even if you don’t cash the check or deposit it to your account until the next year. For example, if the postal service tries to deliver a check to you on the last day of the tax year but you aren’t at home to receive it, you must include the amount in your income for that tax year. If the check was mailed so that it couldn’t possibly reach you until after the end of the tax year, and you otherwise couldn’t get the funds before the end of the year, you include the amount in your income for the next tax year.

It describes the situation where if the postmark is December 31st and there is no way for you to get it before the end of the year the income is treated as being in the next year.

The question to be asking is how would your employer record the event, and if you disagreed with that recording what could you do?

When looking at the charitable deduction deadline, the charity doesn't rally care which year it gets assigned. It has zero tax implication for them. But money being returned to your employer could make a difference for them, and we know it does make a difference for you.

I wouldn't push it too close to the deadline.