Reid Cycles Vintage Ladies 7-Speed Classic Questions & Answers

Reid sells replacement wheelsets for $70 (you get both wheels). But there's nothing to peel off the braking surface: these surfaces are bare alloy. Anything peeling off is therefore some kind of contaminant. I'd recommend taking it into a bike shop so a mechanic can take a look in person and advise.

Additionally, the wheels on these bikes don't have cassettes; they have an older (rare now) setup called a "freewheel". Although these look like cassettes, they're not interchangeable with them. So to fit a different wheel, you would either need a wheel that could accept the freewheel from this bike, or you would need a conventional ("freehub") wheel with a 7-speed cassette. I think these rims are also wider than a typical road bike rim, to take the wider tyres these bikes use.

So, in short, my guess is that there's nothing wrong with these wheels that cleaning won't fix; and that if they ever need replacing you're better off with the Reid parts.