I know this page is around a ZXE600 but it looks like its the same model setup as a ZZR600
http://www.rjfilms.com/blog/greenmagic/valve-adjustment-kawasaki-zx6e-how-to-diy-step-by-step-instructions/
Removal
-Remove the center bolt (12mm) first. This will release an under pressure spring and pin and copper washer with the bolt. Place aside.
-Remove the two outer bolts (10mm) now and remove the CCT housing from the engine. I had to whack mine with a rubber mallet, it was stuck in
there pretty good. It popped out with some energy.
Rebuild

-Once the caps are tightened to 12 NM (104 inch/lbs) of torque, YOU MUST reset your CCT. If you put it back in as it was you will likely
break something and cause damage. Reset it. You do that by pressing in
the little button and then pushing back the little “plunger” (foot
thingee) back into it’s holder. I’m pointing to the ‘button’ you
depress to push the plunger back into the housing.Adjust valves ZX6E
kawasaki-CCT reset button point This pics shows the ‘plunger’
retracted after resetting it: Adjust valves ZX6E kawasaki-CCT
retracted foot
-Now re-install the CCT housing, the raised arrow on it aligns horizontally at the top (but not pointing ‘up’).
-Bolt in those two 10mm bolts on the housing.
-Reinstall the bolt, copper washer, pin, and spring into the CCT housing. It will be tad difficult as the spring will push back on you,
but get the bolt in and tighten to 9.7 NM. This will now engage the
CCT to put pressure on the chain.