I recently learned the hard way that a Scotch-Brite pad can scratch glass. My car, and particularly my windshield, were covered in tree sap. The Scotch-Brite pad got the sap off the car, but it left behind several shallow scratches. The windshield had turned foggy in the spot the sap used to be.
Sand with Cerium Powder
Glass, like metal and wood can be sanded and buffed. The shallow scratches in my windshield needed optical grade sanding.
This is a fancy way of saying that there were no deep scratches and that I could start with the smallest grit of sanding substance available. If your scratch is deeper, you might have to start with another method. The last step in any process will be buffing with Cerium oxide powder.
Cerium oxide powder is a fine grained material used all over the world for buffing glass. It is used all over the world to polish mirrors. I purchased a kit for my drill that included a sanding pad and enough cerium powder to fix several cars worth of scratches.
Application was easy, but messy. Sanding glass must be done wet. Otherwise too much heat is generated.
Begin by masking off the area you want to sand on the other side of the glass. Painter's tape, packaging tape, or any other type of tape will do.
Mix a small part of the cerium powder with water and apply it to the surface. Mount the buffing wheel in your drill. Start the drill slowly and in contact with the cerium slush. This will limit splatters. Bring the drill up to speed and proceed with the buffing operation.
How long the area must be buffed depends on the scratch. The average barely visible scratch will take minutes to remove. Periodically stop and check your progress. Reapply cerium powder as it is consumed.
It's best to keep the buffing wheel close to the affected area. The cerium powder won't create scratches in otherwise pristine areas. If the buffing wheel picks up debris, however, the wheel can create scratches.
In my case the result was a perfect finish. There were no scratches left. The glass looks brand new. There are no distortions in the surface either, which can appear when too much material is removed. The windshield feels perfectly smooth again.
I recommend that you wear work clothes when working with Cerium powder. The drill will fling the slurry all over place. The process, however, is very easy to do. You can use it on windows as well. Cerium powder is your way to buff scratches in glass.