There's a fair chance that the "scratch" is not, in fact, a scratch (meaning material has been either reshaped or removed from the lens) but instead material deposited on the lens. I have seen that numerous times, and after mentioning it to a couple of people on the forum here who were fretting about a scratch they were able to clean the "scratch" off their lens.
A very close examination of the lens in question, using a 10X magnifier, could reveal that the lens is quite a deal after all.
SkipD:
That's a very good point - two years ago while pusing my grand-daughter in a plastic swing, it bobbled and hit my coated plastic eyeglass lens. "Damn, I said, I have a scratch on the lens".
Several weeks later, after routine daily washing with soap and water and drying with a towel, I couldn't find the scratch. It had washed off. It wasn't a scratch, but a deposit of poly plastic from the swing.
Coatings on lenses (even plastic lenses) can be very tough. The OP could check this out.
On the other hand, I personally wouldn't bother - if it has been struck with something to make the "scratches" what other damage has occurred - like lens misalignment?




