Since there is no standard procedure called “change tax year to 2021”, I am guessing as to what the bank is doing. You will have to confirm this with the bank if you have questions.
What I am guessing the bank is doing is withdrawing the excess from your account for 2020, putting that money in their pocket for a minute, and then taking the money out of their pocket and putting it back in your account as a 2021 contribution. Two separate transactions with the exact same result as if they mailed you a check for the excess and you mailed them a separate check for a 2021 contribution, without the hassle of actually mailing checks.
In that case, you will tell TurboTax that you withdrew the excess for 2020. At the end of 2021, you would expect to receive a 1099–INT statement for the interest earned by the excess amount. You would report this interest income on your 2021 tax return. You would also include the re-deposited amount as a 2021 HSA contribution along with any other HSA contributions you make during 2021.
Just remember that you may need to reduce your other 2021 contributions so that your total contributions including the redeposited amount don’t exceed your 2021 limit.
