"on her SS Statement for the year she is paying Medicare premiums."

Yes, from 65, if you are eligible, you can get Medicare. But your Social Security isn't available for deduction if you choose to delay filing to age 70, so you pay for Medicare separately, such as out of your HSA (B, D and Advantage). The deduction is a banking convenience, not a Benefit.

"Tell me more..."

That's not much more to tell. It's a benefit based on earnings, so if you don't pay, you don't get to play. If you keep working and paying in, it is used in the computation for your benefit (and a spousal/survivor benefit).

It's very confusing that she did submit SE, and contributed in the past, and is collecting, and now doesn't want to contribute, but will still keep collecting while also still working but with earnings she doesn't want considered for collecting against.