Cerium oxide can be purchased at a number of online retailers including Amazon and Walmart. Cerium oxide is used to remove scratches from glass and also to polish stones.
Cerium oxide comes in powder form and is mixed with water to form a paste. A polishing pad can be used to buff the scratched glass. The glass will get warm while buffing, but if it gets too hot it is important to stop and let the surface cool down. Cerium oxide is not effective on deep scratches.
In order to easily identify the area that needs to be buffed, mark the underside of the glass with a crayon.