If there is no shim at all other than the one in the pic then yes put it back in with the springs. There is usually a thin shim even with stock springs to keep the steel spring from gouging into the aluminum head but judging from the thickness of the one in the pic it's probably there to boost spring pressure and or get spring at correct installed height. Someone please correct me if I'm wrong.
There is already a thin shim, you cant see cause the spring is sitting on it. so it was doubled up on top of that.
My machine shop guy said that if anything we should put the shim under that whole assembly (spring/keeper underneath on the head directly) he was saying if we put it on top, the spring wont have anything to sit on and will be shifting in place rather than stable on the seat, at least thats what he says for cars.
so what are your guys' thoughts.