Scratches in glass come in different depths and sizes. With the right polish, you can remove scratches that are at or near the surface of the glass. Deep scratches require either professional help or replacement of the glass. Determining whether you have a surface scratch or something more serious can be tricky. If in doubt, however, try removing the scratch manually. Even if the scratch is not fully removed, you still may be satisfied with the results.
Apply a dab of jeweler's rouge onto a lambswool cloth. Polish a small surface scratch until it comes out. This may take several minutes and perhaps longer. You may have to add a dab or two of rouge while you polish. Hand polishing like this is only recommended for the smallest and lightest of surface scratches. You can also try whitening toothpaste as an alternative to jeweler's rouge.