I have used BonAmi for decades. It is less harsh than Comet but seems to attack stains well. It will not scratch the surface of your sink.

Bon Ami generally is successful but sometimes it needs to rest in place for a bit.

Thanks to you both! I can now recall Paul Harvey declaring on his radio show, "Try Bon Ami, good friend!". Yes, I'm an old hoot.

Blue stains usually mean copper in your well water. Avoid harsh abrasives that scratch the glaze. Instead, mix baking soda and hydrogen peroxide into a paste, let it sit on the stain for 15 minutes, and wipe gently.