Possibly getting above my paygrade here, but...
My sense is that physics sees QM as 'more fundamental' than GR, in the sense that inconsistency between the two is to be resolved by absorbing GR into QM. This makes intuitive sense to me, as the glaring problem with GR is that it produces singularities. If you introduced Heisenberg-style uncertainty to spacetime, you'd expect this problem to naturally disappear, as there would no longer really be such a thing as a well-defined point in spacetime, so a singularity simply becomes impossible.
Once you go down that path, then, gravitons are more or less inevitable.
Now my extremely limited understanding is that mathematically, gravitons in quantum gravity act like quantizations of spacetime in the same way that photons act like quantizations of the EM field. As a result, they produce the apparent curvature effects, in the same way photons produce apparent forces between charged particles.
The difficulty of course, is that word mathematically. My mathematical learning (and possibly my innate ability to understand) gets me to (Feynmann-style) relativistic quantum mechanics, and standard general relativity - neither of which I found easy at all. I don't think I have any real hope of properly understanding the maths involved in quantum gravity, particularly not while holding down a full-time finance job.
That's my understanding too, although to understand the mathematics better I am looking at
getting a strap-on auxiliary brain pack...
In one of his books, Roger Penrose gave 3 possibilities:
1) The majority view: gravity is ultimately quantized approaching the Planck scale.
2) The minority view: gravity & curved spacetime is fundamental, and particle physics
can ultimately be described by spacetime geometry.
3) An outside possibility: gravity and quantum mechanics are fundamentally different
phenomena and although it might be possible to find some mathematical way of unifying them, it won't
make physical sense.
As for #3, I am reminded of string theory, which appears to incorporate gravity, but at the cost
of requiring at least 10 dimensions and having a "landscape" of 10500 vacuum solutions.