First, each HSA is owned by one person, there are no joint accounts.
Second, the contribution limit is an annual maximum, it doesn't matter when it is paid, just the total amount. (If you became ineligible on April 1, 2020, then your maximum is $2050. It doesn't matter when it was contributed. You could even contribute the entire amount after your 65th birthday, as long as you don't go over the annual limit.)
You are eligible to contribute to an HSA until the month you are covered by Medicare, not 6 months before. For people who delay starting Medicare, it is effective retroactive by 6 months, but if you join Medicare when you turn 65 and are first eligible, your coverage date is usually the 1st day of the month you turned 65. Your coverage date is printed on your Medicare card.
If you turned 65 on April 2021 (you said "this year"), then you were fully eligible for 2020. If you were covered by a family plan, your eligibility was $8100 ($7100 plus $1000 catch-up provision). If your wife is covered by a family plan and does not have disqualifying coverage, she can also contribute $8100 ($7100 plus $1000 catch-up provision). However, your overall combined maximum is $9100 ($7100 plus the 2 catch-up amounts).
For 2021, your eligibility is $2050 ($8200 x 3/12). Your wife's maximum is $8200, and your overall combined maximum is $8450 (your wife's $8200 plus 3/12 of your $1000 catch-up).
If you turned 65 in 2021, you have nothing to amend, unless you want to make an additional contribution to get your wife's account up to the annual maximum to get the tax deduction. You would then amend to report the additional contribution and claim the tax deduction. You must tell the HSA bank before you make the transfer that this is a 2020 contribution, not a 2021 contribution. The deadline to do this is May 17.
If you meant in your question that you joined Medicare in April 2020, then the concept is the same, the number is slightly different. Your eligibility would be $2025 and your wife's eligibility would be $8100, and your combined maximum would be $8350. You would need to remove any excess contribution from your account (excess over $2025) before May 17. However, you can make a tax deductible contribution to an account in your wife's name up to your combined annual maximum.
In Turbotax, you have to report that you had disqualifying coverage starting April 1 (you are asked to check boxes for the months when you and your spouse had a qualifying HDHP. You have to check "No" for any month when you were disqualified by Medicare. The question should be understood as "check the box if you had a qualifying HDHP and nothing else". If you check that you were not eligible, Turbotax will calculate the contribution limits, and will advise you to remove the excess or pay a penalty. You could also take that excess and re-deposit it into an account in your wife's name as a 2020 contribution and take the deduction (if you are not over the overall limit).
