The whole point of general relativity is that there doesn't need to be a particle that does something, but that gravity is just an emergent property of space. So no, we don't know that a gravity particle has to exist.
The problem is that we have two formulations of physics. Basically, gravity and everything else. Theories such as QCD, QED, etc give rise to quantum mechanics, electricity and magnetism, etc. In these theories + and - charges for example feel an attraction to each other due to an exchange of "virtual" particles. General relativity is based on geometry as you say. Physicist would like to have one framework to describe everything--that's why it would be nice to find a graviton.