[gliese1337]

  Can "gravitons" pass though Earth?

Yes. And the fact that there is no complete theory of gravitons doesn't really matter. It is sufficient to know that scare-quoted "gravitons" (which may be real fundamental particles or may simply be mathematically convenient pseudo-particles corresponding to a classical gravitational wave) can pass through the Earth.

They must be able to do so, for essentially exactly the same reason that neutrinos can: they couple extremely weakly to matter. Which should not be a surprise, because gravity is such a relatively weak force- weaker even than the eponymous "weak force". The fact that neutrinos couple so weakly to other matter is also why they are so dang hard to detect. Meanwhile, gravitons / gravitational waves couple even more weakly to matter, and thus are correspondingly even harder to detect than neutrinos, and pass through solid matter even more easily.

Annoyingly, if it were easier to detect them, that would necessarily imply that the Earth is less transparent to them, and vice-versa: they harder they are to detect, the more transparent the Earth must be. Because, if the Earth were not transparent to them, then that entails that there are materials in the Earth that interact strongly with them, and we could use those materials to build a better detector!