A diamond pad protocol on a grinder will probably get them out, however, matching the factory finish will be problematic. You can replace the sink in half a day.

Try washing it with warm water and non abrasive dish soap. Once dried, take a rag with mineral oil and polish the entire sink (don't use too much oil, just a light layer). I always did this at night and let it sit overnight, and in the morning, the sink was as good as new and the mineral oil kept these pesky rings at bay for a while until it wore away and it was time to polish it once again. When I figured this method out, it was much easier to maintain and I loved that sink! I gave it to my mom-in-law when I remodeled my kitchen and she still raves about it's quality to this day.

Good luck!

Thank you Lynn. I used blue dawn a couple times and it seems to have pulled it up. Thankfully! Do you know what the purpose of the mineral oil is for? I’m seeing a lot of people say they do this… just to keep these ring stains away? I’m assuming it’s caused by water?

Correct! For me, I was tired of seeing ring stains constantly, so polishing with the mineral oil helped keep them from forming much faster. It was quite a while before water rings would start to show so I wasn't constantly wiping the sink down.