Hi -
Drain the bowl and use a "Magic Eraser".
The bowl probably is not "scratched" just has some superficial marks. This happened to us a few years ago and I lived with it until one day I tried the above.

PRESTO! makes me wish I would have tried it earlier... used to drive me crazy!
It will also take the "scuff" marks off of dinnerware that come from eating utensils.
Let me know if it worked!