Glass Art rouge is very useful in removing scratches from glass. Take some jeweler's rouge on wool and polish the scratch in circular motion. Do not put any pressure on the glass or you may end up cracking or breaking it. After a few minutes clean the rouge to see whether the scratch is healed. Now mix some ammonia with water.
Make sure to use gloves and safety glasses while handling ammonia. Clean the surface with this mixture and later, dry it with a towel.