Wow, those tapes look cool, I didn't know such solution existed.
Normally done with a hot bar sealer, but doable if you have a temperature controlled iron and set it around 150C to melt the plastic back to the clean board.
That didn't work at 150°C, I'll try to up the temp a bit tomorrow when I have more light to work.
By tearing off that ribbon cable, you destroyed it beyond repair. Conductive traces from the cable remained on the PCB, what left on the cable is insulated from the both side and therefore is not accessible. And you won't be able to remove the insulating layer without damaging the traces anyway. So just buy another scales.
Resistance of the black traces is a few hundred ohms when the probes are 5 mm apart. Is that congruent with the insulation you're talking about?