  The total mass of the Local Group (LG) is a fundamental quantity that enables
interpreting the orbits of its constituent galaxies and placing the LG in a
cosmological context. One of the few methods that allows inferring the total
mass directly is the "Timing Argument," which models the relative orbit of the
Milky Way (MW) and M31 in equilibrium. The MW itself is not in equilibrium, a
byproduct of its merger history including the recent pericentric passage of the
LMC, and recent work has found that the MW disk is moving with a lower bound
"travel velocity" of $\sim 32~{\rm km}~{\rm s}^{-1}$ with respect to the outer
stellar halo. Previous Timing Argument measurements attempt to account for this
non-equilibrium state, but have been restricted to theoretical predictions for
the impact of the LMC specifically. In this paper, we quantify the impact of a
travel velocity on recovered LG mass estimates using several different
compilations of recent kinematic measurements of M31. We find that
incorporating the measured value of the travel velocity lowers the inferred LG
mass by 10--12\% compared to a static MW halo. Measurements of the travel
velocity with more distant tracers could yield even larger values, which would
further decrease the inferred LG mass. Therefore, the newly measured travel
velocity directly implies a lower LG mass than from a model with a static MW
halo and must be considered in future dynamical studies of the Local Volume.
