I post this pretty frequently for chirping. Stock setup, the throwout bearing is preloaded onto the clutch plate fingers. This causes it to wear out much too soon. Aftermarket quadrant / adjuster setups typically leave an air gap, which is much better for the throwout bearing. However, there's nothing in the mechanism to maintain that air gap. So the fork will move back and forth giving you that chirping noise. The throwout bearing may be perfectly fine. Your cable may be perfectly fine. There's just nothing holding that air gap unless your input shaft is really grimy.
You'll either want to preload like the stock setup (if you have a stock cable and quadrant, pull up on the pedal to have it re-adjust, if the cable is bad replace it). Or if you have an aftermarket quadrant / firewall adjuster or adjustable cable, you'll want to install a return spring to push the fork away from the pressure plate fingers to maintain that air-gap and eliminate the chirping.
When I post this I usually get responses like 'mine doesn't do that.' That either means you don't have an air gap, or that your input shaft is coated with dirt and is keeping the throwout bearing from bouncing around. From an engineering standpoint, in the non-stock / non-preloaded (better) setup, the fork needs something to pull it back if you want to maintain the air gap. A return spring does the trick.
They used to make a kit for this, but any right-sized, not-super-stiff compression spring installed between the housing and the fork will do the trick. Here's a link that helps explain what I'm talking about.
https://www.svtperformance.com/threads/ldc-chicago-clutch-freeplay-correction-kit.170779/ (It was advertised as taking up the slack on the clutch pedal top-side to keep your pedal from rattling if you keep an air gap, which it does, but it also completely eliminates chirping with an aftermarket quadrant and adjuster while maintaining a proper air-gap).
I hate to think of how many cables, TOB's, and forks have been pulled out because of the chirping when they were actually fine. This is just a less-known element to replacing the stock setup with aftermarket (non-self-adjusting) components that most people don't know is a really good idea.
Edit: to clarify, I don't believe that kit is available any longer. I bought mine about 7 or 8 years ago. But you can use the pictures as a guide to what to pick up at the hardware store.