I wouldn't at all assume every piano has dampers like those, either...
ideally, they have felt, that might look like dirt, if the felts are old
and dirty enough.
Well, such persistence could land someone a job removing old felts from
the dampers, so new ones would have such a well-prepared surface for the
new ones. ;)
I don't know whether that's what you did, but the idea of it is funny.
As far as keys with hard-to-remove stains, I'd leave the stains there
and hope time and playing on them faded them. If the piano is old and
the keys look good, they would likely be plastic replacements. It's easy
to imagine making them not just worse, but more permanent than the
Crayola markers did.
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