Deep stains on wood tables

Just got back from long trip, and found that friend who was watering indoor plants had allowed water to seep onto beautiful wooden (alder) coffee table, and into inlaid end table (not sure what wood).
Stains are very deep. Not just water, but have carried into the wood the color of the fabric? synthetic?) "feet" that supported the saucer. Blue-ish stains.
I tried 00 steelwool with furniture wax, but no effect.
Then was stupid enough to try very fine sandpaper, equally useless.
I doubt if I can afford to refinish the coffee table, and the end table, with its inlays, would also be very expensive.
After going online with the appropriate keywords, and finding nothing applicable, I throw myself at your feet <g>
Any experience/recommendations eagerly awaited.
Clueless
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wrote:

Use a small dab of mayonnaise on a rag, and rub the water mark. It would be helpful to know the finish. I recommend refinishing the piece, but if that is completely out of the question you can buff the piece with Johnson's paste wax or Briwax. Briwax comes in several colors and you can find it at woodworking stores or sometimes a hardware store.
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