The black part is just tape. I believe it's just to protect the contacts but it's not integral to the ribbon cable.
Be extremely careful when removing the tape because it's still sticky enough to rip the ribbon cable away from the circuit board. I've personally made that mistake and ruined a perfectly good calculator. I'm not sure you can use isopropyl alcohol or a heat gun without damaging the ribbon cable further.
Unfortunately TI designed these to be so unrepairable that nobody has ever found a easy permanent solution, especially not for the fine ribbon cable. Typically the solution is to just solder wires in place of the ribbon cable.
There's a long standing topic for repairing the TI-83 Plus which goes into many of the repair attempts: https://www.cemetech.net/forum/viewtopic.php?t=5161