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First try placing a tea towel over the affected area. Set your iron to a low setting and iron over the tea towel. Don't stay in one place too long. Keep the iron moving. Leaving the iron in one spot will burn the fibres of the wood and you'll get a dark spot. Check your table often and repeat until the water stain is gone.
The second approach is to use a hair dryer. Set the dryer to its low setting and run it over the water stain in a back-and-forth motion. Again, don't be tempted to stay in one spot as extreme heat could damage the surface. Keep waving the dryer over the water stain until it fades away.
Another option is to use Feast Watson 250ml Surface Restore. It's a combination of waxes and oils that restores worn timber finishes without the need to sand or strip. Please make sure to rub in the direction of the grain and not in a circular motion. - EricL
If the marks have penetrated deeply into the coating, you're likely going to need to sand it back to remove them before re-applying a finish to the table.
Have you tried polishing the area? You could even try some fine steel wool to see if you can remove the mark. The area will become dull, and you'll need to polish it to restore the sheen.
If you decide to go with a complete restoration, you'll find this step-by-step guide useful: How to restore wooden furniture. - MitchellMc
