I don't have a lot of experience with this. My first thought would be to sand it off... However - I do get a woodworking magazine. The issue my wife just handed me has this: "Repair a water-damaged finish". The author Kevin Southwick - is a wood finishing specialist and furniture restorer in Minneapolis, MN.

He opens his article with the following:
"Watering a potted plant can be disastrous if the plant lives on top of something made out of wood. We've all seen the white spots and black rings that can result when water seeps through the pot. And if you've ever tried to sand out these marks, you know it's a tough job that can leave telltale depressions on the surface. Fortunately, in many cases, this type of damage can be almost magically undone by treating the wood's surface with Oxalic Acid. [end quote]

I believe I've heard of this before, when researching refinishing hardwood floors... I know that you can use just plain bleach on hardwood floors (gently) to remove a lot of stains before refinishing.

Anyway - I would suggest doing some more research on refinishing furniture, looking at hardwood floors; and possibly picking up the current issue of: American Woodworker (oct/november 2009) I reference you to page32 for the start of the article which I quoted from above. Hope this helps.