We are just getting to the end of our house sitting and noticed that we had created a white mark on a wooden coffee table - think we must have put a tea bag on it. I know we could just own up to it but first I thought I would check the Internet to see if there was an easy solution.
There is, just put put a cloth over the mark and run over this with a STEAM iron. Within seconds the steam brought the mark out completely. It is so effective you feel like looking round for other marks to use this method on!
I know in our RV / motorhome we had this white effect on the edges of the cupboard directly below the kitchen sink, probably water continuously being splashed there. If you can get the water marks out then regular coating with oil should stop the problem recurring. You would need to be sure you were dealing with proper wood rather than laminate before using this tactic and it may be a little trickier working on a cupboard door rather than a flat surface. Let me know if you try it and it works please.