Electron-beam (e-beam) lithography is commonly used in fabricating metal-oxide-silicon (MOS) quantum devices but creates defects at the Si/SiO2 interface. Here, we show that a forming gas anneal is effective at removing shallow defects (≤4 meV below the conduction band edge) created by an e-beam exposure by measuring the density of shallow electron traps in two sets of high-mobility MOS field-effect transistors. One set was irradiated with an electron-beam (10 keV, 40 μC/cm2) and was subsequently annealed in forming gas while the other set remained unexposed. Low temperature (335 mK) transport measurements indicate that the forming gas anneal recovers the e-beam exposed sample's peak mobility (14 000 cm2/Vs) to within a factor of two of the unexposed sample's mobility (23 000 cm2/Vs). Using electron spin resonance (ESR) to measure the density of shallow traps, we find that the two sets of devices are nearly identical, indicating the forming gas anneal is sufficient to anneal out shallow defects generated by the e-beam exposure. Fitting the two sets of devices' transport data to a percolation transition model, we extract a T = 0 percolation threshold density in quantitative agreement with our lowest temperature ESR-measured trap densities.