string trimmer slits bottom screen door
I solved a similar problem (cat scratching a low screen) by attaching a piece of clear acrylic plastic to the frame, just high enough to prevent damage, and still allowing ventilation through the upper part of the screen. I would guess 8 - 10 inches across the bottom would be sufficient to guard against string trimmers.

My frame was wood, so drilling some holes for screws was easy. Might be harder if you have aluminum. Also, the cut edge of the acrylic was not especially nice looking.