If the screw is turning but not coming out, the plastic tab that it screws into is probably damaged or broken. You’ll need to try to pry the screw out with tweezers as you unscrew it. It is not the end of the world if you can’t screw these back in during reassembly.
I also reconnected this connector before screwing the reader down. You will not have to contend with the pressure from bending the stiff wide cable leading from the connector.