As per Ranger over on CorvetteForums:

http://forums.corvetteforum.com/c6-z06-discussion/2250372-clutch-pedal-issues-how-to-prevent-and-cure.html

Dude thanks!

Never knew about this... Check it

mine like 2 hrs ago :



was gritty inside

now after like 6 flushes.. Will do again before Cayuga :

Just an FYI: Simply swapping the fluid in the reservoir and pumping the clutch doesn't purge all the crap in the system. It still mixes
with the dirty fluid in the supply line and slave (as you can see from Bob's second photo).

The best way, and fastest way to get clean fluid into the clutch master/slave is to follow the directions mid page of his write-up:

Clutch Bleed Procedure Using Remote Bleeder and a Helper

Getting to the bleed valve is a pain unless you have a hoist, or can raise the car with jack stands. It's a two person job unless you have a pressure
bleeder. Even then, a second person speeds up the process.

even then the heavy shit in the slave is still going to be in the bottom. since the bleeder is at the top.