Some copper coins were corroding behind the tap of my bathroom sink. They started corroding and left behind some sort of residue which is hard to remove. How do I get rid of it?
Vinegar is well-known to remove rust and corrosion from materials, and it's completely safe for you and the counter.
Liberally apply white vinegar to the area, let it soak for about an hour, and scrub it with a toothbrush. Abrasive sponges (as seen below) work very well.
Or take half a lemon, dip the cut side into table salt, and rub at the marks with that. Should work on the porcelain, though you may have to repeat it, not sure about the metal tap.
Barkeepers friend, an oxalic acid based cleaner is stronger than those solutions, and should work if they don't remove it entirely.