You just have to enter the contributions in the Deductions & Credits section of your 2020 tax return and make sure the contribution is sent to your HSA by the due date.  You can make contributions to your HSA for 2020 until May 17, 2021.

Just tell TurboTax you will make the contribution, and then don’t forget to actually make it. You will also have to let the bank know before you mail the check or initiate the transfer that this is a 2020 contribution and not a 2021 contribution.  You will not get any paperwork for this, you simply report the amount you actually contributed. When the bank sends the form 5498 to the IRS later in the year, they will compare your tax return with the records, but you don’t need any paperwork to file your tax return and declare the extra contribution.