I know exactly what this is. I had the same problem for 5 ******* years before I got some help from a Jeep Expert at a local dealership. (The guy lives and breathes Jeeps, and owns 7 of them.)
Before this got fixed, I swore the problem was the master cylinder, slave cylinder or linkage. I sprayed WLG inside the bore, on the linkage, the works. Sometimes it seemed to make it better, sometimes not. Always worse when cold. Sometimes it went away for months at a time. Sometimes, it was a "scrunch" or a "screeching" noise. Sometimes a snapping or light popping sound, with resistance felt in the pedal, and only on the last 1/4 of pedal travel near the floor.
It drove me nucking-futs for a LONG TIME.
I finally put the Wife in the driver's seat and had her work that pedal. Sure enough, the sound was coming out of the bellhousing.
The local transmission guru swore it just needed some Goose-Grease on the pedal crosshaft. It did not. He recommended replacing all of the hydraulics, and I did. The problem went away for exactly one week, at which point my mood turned decidedly homocidal.
I finally gave up and sought the advice of a known expert, which is what I recommend to the OP to verify. He correctly diagnosed the problem in 5 seconds. Experience is everything.
The problem turned out to be a broken clutch fork ball pivot. (See diagram.) OEM cost was $19, and $450 in labor to tear it apart and replace the damned thing. It had been broken since it was brand new, and for whatever reason, I never bothered to have it repaired under warranty.
It won't break completely leaving you stranded, but it will drive you up a wall until you get it fixed. Vaya con dios...
Note: this photo is not of MY Jeep. My horse is cleaner now than when I bought the thing new. If your bellhousing is this dirty, you have bigger problems than can possibly be remedied by all of Mankind.
Some experience the squeakpoint at the end of the clutch slave pushrod, but in my case, it was the ball stud at the other end of the clutch fork. It MAY be either one -- have it checked out and repaired before you lose your mind.