Analyses of Fermi Gamma-Ray Space Telescope data have revealed a source of excess diffuse gamma rays towards the Galactic center that extends up to roughly $pm$20 degrees in latitude. The leading theory postulates that this GeV excess is the aggregate emission from a large number of faint millisecond pulsars (MSPs). The electrons and positrons ($e^pm$) injected by this population could produce detectable inverse-Compton (IC) emissions by up-scattering ambient photons to gamma-ray energies. In this work, we calculate such IC emissions using GALPROP. A triaxial three-dimensional model of the bulge stars obtained from a fit to infrared data is used as a tracer of the putative MSP population. This model is compared against one in which the MSPs are spatially distributed as a Navarro-Frenk-White squared profile. We show that the resulting spectra for both models are indistinguishable, but that their spatial morphologies have salient recognizable features. The IC component above $sim$TeV energies carries information on the spatial morphology of the injected $e^pm$. Such differences could potentially be used by future high-energy gamma-ray detectors such as the Cherenkov Telescope Array to provide a viable multiwavelength handle for the MSP origin of the GeV excess.
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