Quantum gravity: vertex correction

In QED, the classical vertex correction is due to the fact that the energy of the far field of a charge does not have time to take part in the scattering process. This reduces the effective mass of the charged particle.

This is related to bremsstrahlung, in which the far field, and some of its energy, is "freed" from the charge.

In gravity, bremsstrahlung has a 16-fold energy compared to the analogous electromagnetic system.

What kind of an effective mass reduction, if any, could be happen in the vertex correction for gravity?

Does a mass reduction matter at all, if the inertia of the particle is reduced as much?

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