should have put中的have可以去掉吗

You should have put the book where you found it. 请问这句话中，have可以去掉吗？它干什么成分呢？

You should have put the book where you found it

本句中should have done表示本该做某事而未做。即你本该把书放回原处。（实质放到别处了）

should do 则表示应该做某事：

You should put the book where you found it. 你应该把书放回原处。（还没放）