We describe a new, more accurate procedure for estimating and removing inner zone background contamination from Van Allen Probes Magnetic Electron Ion Spectrometer (MagEIS) radiation belt measurements. This new procedure is based on the underlying assumption that the primary source of background contamination in the electron measurements at L shells less than three, energetic inner belt protons, is relatively stable. Since a magnetic spectrometer can readily distinguish between foreground electrons and background signals, we are able to exploit the proton stability to construct a model of the background contamination in each MagEIS detector by only considering times when the measurements are known to be background dominated. We demonstrate, for relativistic electron measurements in the inner zone, that the new technique is a significant improvement upon the routine background corrections that are used in the standard MagEIS data processing, which can "overcorrect" and therefore remove real (but small) electron fluxes. As an example, we show that the previously reported 1-MeV injection into the inner zone that occurred in June of 2015 was distributed more broadly in L and persisted in the inner zone longer than suggested by previous estimates. Such differences can have important implications for both scientific studies and spacecraft engineering applications that make use of MagEIS electron data in the inner zone at relativistic energies. We compare these new results with prior work and present more recent observations that also show a 1-MeV electron injection into the inner zone following the September 2017 interplanetary shock passage.