A sliding screen door that sticks, drags, or has torn mesh usually comes down to three things — dirty rollers, a dirty track, or damaged screen. You can fix all three in one session.
Lift the screen door up into the top track, pull the bottom outward, and remove it. Flip it over, inspect the rollers, clean, spray with silicone, or replace if worn. Adjust the roller screw to set the correct door height.
Vacuum and wipe the track clean. Spray lightly with silicone. Put the top of the door into the upper track first, lift up, set the bottom on the lower track, and adjust rollers until it slides smoothly.
Pry up the old spline and remove the old screen. Roll new fiberglass screen over the frame. Press new spline into the groove working one side at a time, keeping the screen taut. Trim excess with a utility knife.