Diamond Polishing Rotary Tools can improve the look of glaze & glass scratches or scars. These are made of a blend of Diamond Grit and stiff rubber down to the shaft.
It is best to first grind off the glaze drip with a DiamondCore Rotary Tool, then sand down the scar with the finest available Diamond sandpaper (800 grit preferred), then start with the most coarse polishing bullet, then to the finer, then the finest bullet to finish. ( do not expect to get the same sheen as when the glaze was kiln-fired, and the more minerals and powdered coloring elements there are in the glaze the less likely to get a high-gloss finish).
Shaft size: 2.3 mm dia. (which may require a collet See "Dremel Collet Set").
9 Piece Set includes 3 shapes in : Black Medium, Green Fine, Creme Extra Fine.
Use all appropriate safety precautions. Always use safety goggles. Keep out of the reach of children.