You might be able to install light rail molding to the bottom of your cabinets, but you'll want it color matched and it will slightly lower the space between counter and cabinet where the trim is. Hoping a pro will chime in about the best way to hide under cabinet lighting for your situation.

I guess they thought they were doing something nicer by giving you a finished underside to your upper cabinets, but they should have left a channel for the lighting, BUT these details should have been discussed before your old cabinets were touched.

Full overlay cabinets with light rail and finished underside with cut-outs for plugmold and LED tape light.

It looks nicer with the finish panel on the bottom. I'm guessing you didn't discuss the undercabinet lighting plan with the cabinet finisher. If they put the finish panel on the underside of the cabinet without removing any of the cabinet structure, there should a space between that panel and the bottom structure of the cabinet. You could cut a slot in the finish panel and mount the LED tape to the bottom structure, maybe in an aluminum C-channel. Rest of finish panel acts as the light bar. Could look very clean. I'd ask them.