Hi
I would peel back the paint with a hand scraper try the ones with a
Stanley blade in but be careful not to damage the wood. As the paint
has not adhered so should not be too much of a problem, then rub down
the old paint surface with sand paper to key surface, prime with
correct primer if needed. Paint with oil based paint.

By the way a vacuum cleaner should be able to pick the peeling paint
up off the floor with no problem. I wouldn't use a chemical paint
stripper too much hassle and can be very expensive at least where I
live anyway


Regards

Alex
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