Lets not ask about how they got there but how can they be removed. This is a real stained wood table not the veneer stuff. Amish made.

Got some really light swirl marks. Need them to go away before the wife finds out. Thanks

How they got there might provide clearer answers. Generic light polishing could be pumice. Barkeeper's Friend, maybe, for a cleanser.

What kind of finish is on the wood?

I believe the finish is catalyzed lacquer (per the website).

I tried to take a smudge off the table with a magic eraser. Don't judge me

I've heard of using walnut shells to blend out the sort of marks you are describing.

Youtube may have answers.

A plastic polish is what I use for lacquer. Even a paste toothpaste would work as a mild abrasive. Auto buffing compound, sometimes.

A local hobby shop would have options.

Novus 2 is what I use on nitro finish.

I clean the surface with naphtha or lighter fluid then use the Novus 2.

Really thick finishes, like on a cheap guitar, I've removed scratches with acetone - fingernail polish remover - but this stuff will melt any thin lacquer. It even melts plastic bindings.