Anti-reflective coating has been a great development in eyeglasses, but it certainly doesn't feel that way when it gets scratched. The reflection may be gone, but the scratch is all that you can see. Luckily, there is a quick fix that you can perform with easily-found household items. Vinegar and mustard work together to fix scratches in the coating. Be warned: it may not work on the most stubborn of scratches, but it is certainly worth a try.
Mix one part vinegar with one part mustard to form a paste.
Apply the paste liberally to the affected lens.
Let the paste dry thoroughly.
Gently buff the paste away with an eyeglass cloth.
Wash the glasses as usual; examine them to see if the scratches have improved.
If this technique doesn't work, you may need to take the glasses to be professionally repaired, or try another tack.