c4 experts advice needed valve body question

It depends on the kit you bought, from your pics it looks like someone put in a competion shift kit already.
On a 66 valve body there is no spring on the Cut Back Valve but in many shift kits a ball is installed and sometimes the valve is ground down a little.
the rubber disc on the lower left is there from stock BUT it is removed in lots of kits.
In a 66 there is no check ball in the center hole. In 64 valve body there is a check ball there.
You didnt say what you intend to do with the car,,, stock ,, or competition and you didnt say what kit you bought.
Buy a good shift kit and not the lowest price kits. I buy the B&M trans pak kits as these kits offer 3 stages in one kit from stock to competion.
The part number you should have bought is 50227.