The water has penetrated the finish on the table top, and stained the wood underneath. It is probably possible to remove the stain with oxalic acid.
But I doubt you can do it in a way that esthetically matches the rest of table top unless you strip and treat the entire surface. You have to remove the finish in order for the oxalic acid to work, and it's nearly impossible to remove the finish from just the stained area, and then replace/match the look of the old finish in just that area - even a slight difference in tone or sheen in the newly finished patch will stand out on the table surface. The bleaching action of the acid may also subtly change the tone or color of the wood, and you'll want that effect to be uniform or very well blended across the table top. If the entire surface is refinished properly though, any difference between the new finish and the edges, legs, etc of the table won't be apparent, as it separated from the old by edge and shadow effects.
If it's really important to you, I would find a re-finisher, restorer to do the work. It's a tough thing for someone with little experience in wood finishing to get right.