Clean the glass using glass/window cleaner, vinegar or lemon juice and a newspaper, finish by rubbing gently with soft type cloth. You then rub in a polish like Brasso, non-gel toothpaste, using small circular motions with a soft cloth, not a J cloth. See how you get on with that, it worked for me. What caused the scratches? Mine were caused by a small puppy and were impossible to just rub/rinse out. If caused by a big dog or cat I don't know if it would work on their tougher scrapings.