Unfortunately, what you see are not water marks, but actual surface damage. Both travertine and marble are calcium based stones and vulnerable to damage from acid (also called etching). To get rid of the etch marks, the stone will need to be polished out, much like a gemstone would have to be if it were scratched. If the etching is not too severe, you can try to resolve this problem yourself using an appropriate polishing compound. (See our Caring For It page for a link to recommended products.) If the etch marks are too deep or cover a large area, your travertine and marble will need professional honing and polishing to get them looking beautiful again.