Yikes that area will have to be scraped down to raw wood, restained, clear coated, then possibly the whole room will get another coat of finish.

No way. I’ll die. I want this to be done. We have an open floor plan - the entire first floor!!!

Is that some kind of bonding glue that was used to affix the trim? Almost looks like epoxy. If your floors were recently refinished and if that's epoxy, it might still be soft enough to un-bond from your flooring finish...perhaps use a hard plastic putty chisel and focus your efforts at the margin of the clear stuff. If the plastic chisel (putty knife) is too soft, switch to a blunt metal putty knife (something like a 2" sheetrock finishing knife) and see if you can find any evidence the clear material may be unbonded from your floor. If it can be unbonded, you will probably have to cut it free from along the trim and that sounds like the most damage-prone part of this suggestion!

No idea. My husband was wondering if the floor isn’t level and it just “drifted” that way after applying the poly.

From the looks of the puddle, that ran out from under the trim. Epoxy gets harder and harder over time but may still be a bit soft now. If it will un-bond from the floor finish, the edge of the puddle where it meets your floor finish is the place to encourage it to let go. If your contractor can be brought back on site, certainly do that before you try anything yourself. They owe you a fix. Oh, sorry, I read again and see you are getting some ideas and input before talking to your contractor. Outstanding!

Thank you John 9a and no way would I attempt to fix this myself! Just trying to figure out what the heck that is. Thank you!

G&S has it right. If done carefully, the finisher can likely tape around the perimeters of the affected boards and recoat them after scraping and sanding the puddle.