How To Remove 'White' Watermarks From Your Furniture:

If the water mark on your wood furniture is white, then you can
probably repair the damage yourself. Black water marks require
much more work because that's a sign that the water has gotten
beneath the surface finish to damage the wood. Here are the
items you will need to remove a white water mark from your
furniture:

*0000 steel wool
*Car Wax (Wax, not polishing or rubbing compound which will
scratch your furniture)
*Scratch remover for cars
*Clean rags, and some
*Cooking oil
James H. Taylor, Wood Furniture Repair and Restoration Information Centre
Pour about 1 teaspoon of oil directly on the watermark, then rub the mark very gently with the steel wool,
moving with the grain of the wood, not across it. Do this for about a minute then wipe it clean to see how
much of the mark you have removed. You only want the scratch the surface of the finish to remove the
mark, so carefully repeat this step, using as little pressure as possible, until the mark is gone. Next, apply
the car wax according to the directions on the can. You need to do this in order to remove the scratch marks
left by the steel wool. You’ll have to do the entire surface in order to get an even sheen.