In this paper we consider non-relativistic matter-wave interferometer coupled with a quantum graviton bath $mathord{-}$ and discuss the loss of coherence in the matter sector due to the matter-graviton vertex. First of all, such a process does not lead to any entanglement, but nonetheless the on-shell scattering diagram can lead to loss of coherence as we will show. Importantly, we will show that graviton emission is the only one-vertex Feynman-diagram $simsqrt{G}$ which is consistent with the conservation of energy and momentum at the dominant order $simmathcal{O}(c^{-2})$. We will find that the resulting dephasing is extremely mild and hardly places any constraints on matter-wave interferometers in the mesoscopic regime. In particular, the show that the corresponding loss of coherence in the recently proposed experiment which would test quantum aspects of graviton $mathord{-}$ via entanglement of two matter-wave interferometers $mathord{-}$ is completely negligible.
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