I briefly worked in this area of physics, it’s complicated and depends on your definition of a particle and which quantum gravity model you’re talking about.
To simplify things you can just ask the same thing about non-quantum gravity. Why does gravity escape the black hole? The painfully mundane answer is that the black hole is gravity, it’s not escaping itself. Gravitational waves can’t be emitted from inside the black hole but that’s because those are a form of radiation and not the structure of spacetime.
This is specifically important because even quantum gravity (the kind with gravitons) still has this distinction. Particles belong to a field and are excitations of it, the gravitational field itself is not made of those particles. The force associated with that field is mediated by gravitons, but what that really means is complicated and honestly possibly just the result of a cool mathematical trick. It also comes with a bunch of crazy behaviour where you have particles that can break the laws of physics by just kinda doing it so quickly that nature blinks and misses it.
The point is, the quantum gravitational field is enough for the black hole to do its job when objects come by, gravitons don’t actually need to escape, though they are involved in complicated ways.