Using clay is strange. Museum putty would have been much better. The common modeling clay has oils and some kind of filler. Can you rub it off with a terry cloth? You may find the finish on the table is more shiny or darker where the clay was. If so, some of the oils probably migrated into the finish and you will need to try to soak it out. The first thing I would try is odorless mineral spirits. Soak a rag or paper towel and place it flat on the surface and wait. Also mix small bits of the putty that you removed with various solvents see what makes it break up.
If nothing works, cover the spot with another lamp? Doily, Candy dish? Or if you really want to save the table, sand it lightly and apply several coats of high gloss varnish and then rub the glossy surface down with rotten stone or pumice to get the gloss level you want.
Good luck,
Bobk