Here is how Medicare enrollment impacts your ability to contribute or use your health savings account.
HSA contributions and Medicare enrollment: Not permitted
Here's what the IRS says in Publication 969, Health Savings Accounts and Other Tax-Favored Health Plans.
IRS note on enrolled in Medicare
Beginning with the first month you are enrolled in Medicare, your contribution limit is zero. This rule applies to periods of retroactive Medicare coverage. So, if you delayed applying for Medicare and later your enrollment is backdated, any contributions to your HSA made during the period of retroactive coverage are considered excess.
You cannot be enrolled in Medicare and make contributions to your HSA. If you enroll in Medicare, you must stop making HSA contributions by the beginning of the month that you enroll into Medicare. Keeping with this timeline will ensure that you avoid taxes and penalties.
Centers for Medicare and Medicaid Services (CMS) on Medicare Part A enrollment
"If you qualify for premium-free Part A, your coverage will go back (retroactively) up to 6 months from when you sign up. So, you should stop making contributions to your HSA 6 months before you enroll in Part A and Part B (or apply for Social Security benefits, if you want to collect retirement benefits before you stop working)."
HSA distributions and Medicare enrollment: Permitted
While you can't contribute to an HSA while enrolled in Medicare, you can continue to make distributions (withdrawals) from an already-established HSA for qualified medical expenses. HSA funds are truly your funds!
Source: IRS Notice 2004-2 Q&A 27