Left: Product of overlapping elliptical 2D Gaussians, representing the positional uncertainty of SGR 0501+4516 and Gaia sources in the vicinity, as a function of time. Only sources with 1D radial separations with more than 3σ significance are shown. We find two Gaia objects that meet this criterion (orange and blue). The grey lines are Gaia matches found when the SGR proper motion vector is rotated by 90, 180, and 270 degrees. The ‘real’ matches are not obviously distinct from the false or random matches. Right: Two ‘real’ matches, with their extinction-corrected absolute magnitudes (based on their best parallax distances and extinction at that distance in the Bayestar 2019 dust map) plotted against their peculiar transverse velocity. Their Gaia DR3 IDs are labelled. Binary population synthesis predictions for the properties of stars ejected by the supernova of a binary companion are shown with the grey shading (Chrimes et al. 2023), where each contour moving from dark to light grey bounds 10% more of the probability.