Did he use an oil based or water based paint? What was the cleaner he used? Unless he was your DH, I'd ask him to come back and clean up his mess. In our younger years my DH was a house painter and cleaning up your mess was part of the job--always.
oakleif

my mother in law painted lots at my house, and I a baking soda paste to scrub the sink. after some elbow grease, it comes off. if you want to shine it afterwards, wipe with rubbing alcohol

This was a hired painter (we are building a custom home) and it is water based paint. He did "clean up" it's the leftover residue I'm having trouble getting out. My point is, he should have never used my kitchen sink to clean up. I did try some white vinegar, which was a suggestion on another forum. It did help - I just can't seem to get rid of the faint paint rings. I'll keep trying - not the end of the world - but aggravating. Thanks for your suggestions.

A lot of times white in sinks come from the water. Like calcium lime etc. Also it is safer for a painter to wash their brushes out in a sink than outside with a hose. The paint goes down in the earth and when you wash inside it goes down a drain. Some good elbow grease with baking soda or special cleaner should do the trick. Good luck!

Have you tried using a clean rag with some turpentine on the corner of it. Use a rubbing motion on the paint stain & rinse?