Pull the whole enchilada as a unit... then, when you reinstall it, push and hold forward pressure on it as you tighten the cross bolts evenly. Consistency in installation will ensure a greater likelihood for an accurate return to zero.
I have always been told to push back into the rail slots when installing the rings. It makes it so that recoil does not have any room to push the rings backwards.
Maybe that's wrong, just what I have been told.