Damage to wood table top from plastic table cloth
sand it lightly and use the matching stains. I would use like to clean it with coca cola first with damp cloth with light pressure. Otherwise if the damage is really bad. Do sanding and staining. You can match the stain easily as there are a lot of product are out there for different types and colors of stains. Good luck!
Maybe heat with a blow dryer and try to scrape off.
What sort of damage is it? Has the plastic melted on to the wood?
A picture would help to see exactly what the situation is.
Most likely there has been a chemical reaction between the polymers in the plastic and the polymers in the finish. Many plastics/vinyls are made to be somewhat fire resistant and those things can make it more reactive. I had a dining room table that reacted to a plastic flower pot where the feet touched the surface. Nothing short of refinishing would change the finish back. Spot sanding, staining, and finish rarely look good. If you find you have refinish the top, do the whole top and any leaves you have. But you should try whatever you can to improve the finish. I would suggest you use some Lemon oil to see if that will help blend the damage areas to the undamaged area. Avoid products like Pledge that contain silicone. Silicone will imbed into the finish and make future refinishing problematic.