Dave:
There is no good answer here - without confirming directly with the provider/vendor/maker what was used. I am unfamiliar with Theodore Alexander, and quite frankly was too lazy to follow the site to try to determine. A custom maker can use any finishing options, whereas volume factory production tends to use methods that fit their budget, schedules, and quality requirements. Mass produced, and many custom made pieces, will be spray finished, but even that does not the materials to a very short list. Lacquers, conversion varnishes, polyurethanes, are among the categories that may have been used. You can likely think of more.
Here is what I would do if it were my dining room table (and I do have a commercially made table with an unknown to me finish). I will outline my cleaning process, used before any decision to do something "drastic." Of course if this is heat damage to the finish, cleaning won't address that. If it was a cover or lid with warm water vapor that penetrated the finish, then a good dose of patience is required: 24-48 hours in AC is a good start. Of course if she has used waxes or PLedge or silicone to keep it clean and shiny, then what I suggest below may work, or may not.
Use a water based soap solution (like the cheap dollar store stuff I keep on hand to spray and wipe clean the countertops, really any soap in a spray bottle that does not have solvents or ammonia in it - NO windex!). Spray and wipe with a soft clean cloth. Repeat a few times without letting the soapy water puddle for long on the surface. Dry with a cloth. Then leave it to dry thoroughly (many hours, up to 24, assuming humidity is controlled by AC) - maybe that is all that is necessary. If that worked well, but the remnants are still there, repeat the process.
The next level of cleaning I would use is an alcohol - many people have rubbing alcohol in the house, that works, or maybe denatured alcohol (repeat alcohol, NOT ACETONE). TEST the alcohol first on an inconspicuous place, because a shellac finish (only one I think) would be affected by alcohols. Highly unlikely that a dining room table is finished with shellac as the topcoat, because it is reasonable to expect an alcohol spill on a DR table at some point. If the finish passes this test in an inconspicuous area, then try to clean the spot using a clean soft cloth: wet the cloth and gently apply/wipe. Repeat several times. Allow sufficient time to dry thoroughly before assessing whether anything else is needed. Dry thoroughly means hours not minutes - as alcohols can penetrate the finish without damaging it.
NO abrasive materials or cleaners should be used - nothing containing wax or silicone.
If that does not cleanup the sticky mess, there may be damage to the finish. I'll let others speak to how to deal with that.
Henry
