Observations of the Milky Way (MW), M31, and their vicinity, known as the Local Group (LG), can provide clues about the sources of reionization. We present a suite of radiative transfer simulations based on initial conditions provided by the Constrained Local UniversE Simulations (CLUES) project that are designed to recreate the Local Universe, including a realistic MW-M31 pair and a nearby Virgo. Our box size (91 Mpc) is large enough to incorporate the relevant sources of ionizing photons for the LG. We employ a range of source models, mimicking the potential effects of radiative feedback for dark matter haloes between $10^{8}-10^{9}$ M$_{\odot}$. Although the LG mostly reionizes in an inside-out fashion, the final 40 per cent of its ionization shows some outside influence. For the LG satellites, we find no evidence that their redshift of reionization is related to the present-day mass of the satellite or the distance from the central galaxy. We find that less than 20 per cent of present-day satellites for MW and M31 have undergone any star formation prior to the end of global reionization. Approximately five per cent of these satellites could be classified as fossils, meaning the majority of star formation occurred at these early times. The more massive satellites have more cumulative star formation prior to the end of global reionization, but the scatter is significant, especially at the low-mass end. Present-day mass and distance from the central galaxy are poor predictors for the presence of ancient stellar populations in satellite galaxies.

14 pages, 12 figures, 2 tables. Submitted to MNRAS