Watermarks can happen in all finishes after they have aged and become somewhat porous. The marks appear light gray to white and are almost always very superficial – that is, right at the surface of the finish.
So one way to remove them that almost always works well is to abrade off the very top surface of the finish with fine steel wool or abrasive pad. Usually, the discoloration will be removed with very little effort, as shown in the two accompanying pictures.
The downside of removing watermarks in this manner is that you may change the sheen of the finish, making it flatter or glossier, and there’s no easy way to disguise this.
The first choice would be to blend the sheen of the rubbed area in with the sheen of the surrounding area. Do this by choosing a grit steel wool or abrasive pad that does this well. You can try several times with different grits to try to achieve a match. You can also use different pressures to “feather in” the rubbed sheen.
No matter how close you get however, a rubbed sheen never looks exactly the same as a sheen created by just the finish because a rubbed sheen is composed of scratches.
To get the entire surface, almost always a tabletop, uniform, you’ll need to rub the entire surface with the same grit abrasive. You could also apply another coat of finish on top. The least risky, if you don’t know the finish you’re working on, would be shellac, or wiping varnish padded on.