I would take it out, or at least some of it (like maybe outer 50%?_ Grass and weeds are incredibly helpful in holding hardware cloth flat on the ground.
Might also help, if you have soft soil, to pound a few landscape pins interlocking at an angle, and in alternating directions, and have those at key points like corners to try and lock them down a bit more. Like put one in 45 degree slanted towards the fence, then the next at 45 degrees slated away from fence. Um, it's like putting bobby pins in your hair and having them crisscross to hold each other in place?
Window looks fine.