How to polish the lenses of scratched reading glasses?

The lenses are make from plastic and no extra coatings to provide scratch resistance, it is that easy to scratch. If you want remover the scratch on plastic lenses, Abrasive cleaners should never be used on plastic lenses, don't use the toothpaste or car polish because it may make your lenses scratch worsen.

As suggest
If they are prescription reading glasses, take it to where you get a reading glasses they may get the scratches out for you. or clean with soft towel and only with recommended lens cleaner. The microfiber lenses cloths are excellent.

Microfiber lens cloth

Find Microfiber lenses cloths at Amazon