The problem is that to be eligible to contribute to an HSA, you must have HDHP coverage, and not conflicting coverage. Medicare is a conflicting coverage. So even if you still have your HDHP coverage but also have Medicare in a given month, you have to answer on the IRS form 8889 (and in TurboTax) that you have "None" for HDHP coverage.
When TurboTax reports on the 8889 that you have "None" for HDHP coverage in a given month, it is literally correct - because the meaning according to the IRS is "either you have no HDHP coverage or you have HDHP coverage but also conflicting coverage". Look at <a rel="nofollow" target="_blank" href="
https://www.irs.gov/publications/p969">https://www.irs.gov/publications/p969</a> and find "Qualifying for an HSA" to see the discussion about HDHP coverage.
This does not affect the Health Insurance part of the interview, where you indicated (correctly) that you had health insurance for the entire year.
