100 percent acetone. Unfortunately it will most likely damage your dining room table's finish as well.
Suggest using 100% cotton swabs with paper stalks (like Q-tip brand), and use it sparingly. A one-sided razor blade, or similar scraper may help also when you have softened it to lift it off and saving some of your table's finish..remember in this case (removing the glue but attempting to do the least damage possible to your table's finish) you want to go by the rule "more is less" regards the acetone.
Acetone is available in small quantites as regular (not the pink non-acetone version) nail polish remover, you very well may have some in the bathroom presently!
Have some 100% cotton cosmetic pads handy for quick lint-free removal of any residue before the acetone has an opportunity to additionaly damage areas of your table's finish and stain. Then of course, sadly, is the task of restoring the finish in said area.