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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.