The black part is your cable slide and it's supposed to slide back and forth on the cable guard rod. You've got to clean them once in awhile. Take it off and use alcohol to wipe down the cable guard and put some on a q-tip to clean the inside of the slide.

It should not have any effect on your peep rotation though. That is caused by string and/or cable creep. While you've got the bow relaxed to clean up the slide, go ahead and adjust your string/cable lengths and get your peep oriented correctly again.