That's a bit of a head-scratcher to me. In the pic with the wet body, it does indeed look like two circular "stains", but the ultra close-up I can't see the circular pattern and they look more like grain anomalies.

If it is possibly an oil or grease (either is possible given there is machinery involved in their manufacture) maybe try scrubbing the spots with naptha and a stiff plastic bristled brush (something more aggressive than a toothbrush).

Alternatively, if you have an orbital sander, it may be worth trying to sand them out. If you do this, make sure you sand the whole top evenly so you don't end up sanding a divot in the problem area.

I'm really just throwing darts blindfolded...