Don't pinch off traps. get a pair of scissors and cut just the trap off. You can leave the leaf. It will still help with its photo
If you trigger a trap...it will re-open in a day or so.
And each trap can only take so many opening and closings...after that it will either not work(respond) or the trap will die. Just cut the trap off like mentioned above.
It you don't take off the dead trap...the only thing that would happen is that it would spread to the leaf and then you should remove it at that point. If you let it go further...the leaf will rot and you might get some mold/rot on the rest of the plant.