The Binky Bunny screen lays on top of the litter. A determined bunny could probably destroy/ remove it because it has enough space on each side for a rabbit to get its paws under there. I don’t think it happens often, though, that a bunny bothers the screen. At least I haven’t read many anecdotes on here about that happening. My bun has used her screen without incident for almost a year. The Busy Bunny sells a box that has a screen attached, but it is $30, which is a bit pricey, imo.
As far as the sides being too low on the box sold here, I guess it depends on your bunny’s habits. It’s a standard sized cat litter box, which is about four inches high. Once in a while a bunny will scoot back too far in it and pee over the edge unintentionally. Just be mindful of not piling the litter too high, as Stickerbunny said, and you should be fine. Or just get one with a higher back to begin with.
I’m thinking a bigger box would be much less attractive as a tossing toy, though. Plus, most rabbits just like them better for being roomier. If you’re not already providing her with lots of toys in her cage to toss and shred, you might also try that in addition to the diggy box. It sounds like your bunny has just gotten into the habit of playing with her current box; she likes that she can make a nice banging noise that gets your attention, and that the box comes apart nicely to make a wonderful mess. Lol.