My dear dog, Keziah, is quite large. She doesn't know the strength of her love taps, let alone a paw to screen. She once broke a double pane window going for a squirrel.
(Amazingly neither furry friend suffered drawn blood.) I don't have screen doors on my home, and Keziah has figured out how to open the sliding back door to go out, and press down the front door latch to come back it. She DOES know what doors are for.
Ironically, when she was a 25# puppy she learned she couldn't knock over the gate into my cats' sanctuary. At 90# she could easily do it now, but comes to a screeching halt at the gate, whenever the cats lead chase. I've ordered a similar gate, which I am planning on attaching to the closet wall perpendicular to the door, and opposing wall (next to the fridge), as far away from the screen as possible. Plexiglass was going to be too complicated to attach...not to mention Keziah would have the door latch figured out in little time. And her toes (toenails) would get through any grate.
On order: ALLAIBB Walk Through Baby Gate Auto Close White Child Safety Gates, Ex. 24.0-27.56 in :https://www.amazon.com/gp/product/B0...1?ie=UTF8&th=1
Am hoping she doesn't have enough room to gain the momentum to jump OVER, into a space which she wouldn't fit