Find any raised edges on the scratches and sand them down to the surface of the block, using 400-grit wet/dry sandpaper saturated in water. Concentrate on the raised edges only, taking care not to scratch the rest of the glass surface with the sandpaper.
Cover the lamb's wool polishing pad on your electric buffer with a layer of jeweler’s rouge. Wet the surface of the rouge block, and then place it against the pad. Turn the buffer on low speed to spread the rouge over the pad. Stop the buffer once there’s a visible layer of the rouge present.
Place the buffer pad against the scratched surface of the glass and turn the power of the buffer on to medium. Apply a light pressure with the buffer, smoothing out the scratch so that it’s level with the rest of the glass and disappears into the surrounding block surface. Reapply rouge as needed to keep the pad covered.
Create a cleanser consisting of 1/2 ounce ammonia diluted with 2 cups of warm water. Pour the cleanser into a spray bottle and cover the newly buffed glass with the mix. Remove the cleanser using a lint-free cloth.
Examine the glass for any remaining scratches. Repeat the buffing process for scratches that are still present until you’ve buffed them away.