These are the paddle type latches that have a rod attached to the paddle. When you lift the paddle the rod pushes on a lever that retracts the spring loaded latch. The paddle binds and cannot be lifted. I don't see a screw to tighten other than the pivot screw on the lever, which is tight.
Bones...you may be right about binding on the strike plate, which is a metal piece attached to the bottom of the opening to catch the latch. The latch does not full retract but it is the same amount of retraction on all slam doors. It could be that the strike plate is bent and higher than it was before.