With infrared ellipsometry we studied the response of the confined electrons in γ-Al2O3/SrTiO3 (GAO/STO) heterostructures in which they originate predominantly from oxygen vacancies. From the analysis of a so-called Berreman mode, that develops near the highest longitudinal optical phonon mode of SrTiO3, we derive the sheet carrier density, Ns, the mobility, μ, and the depth profile of the carrier concentration. Notably, we find that Ns and the shape of the depth profile are similar as in LaAlO3/SrTiO3 (LAO/STO) heterostructures for which the itinerant carriers are believed to arise from a polar discontinuity. Despite an order of magnitude higher mobility in GAO/STO, as obtained from transport measurements, the derived mobility in the infrared range exhibits only a twofold increase. We interpret this finding in terms of the polaronic nature of the confined charge carriers in GAO/STO and LAO/STO which leads to a strong, frequency-dependent interaction with the STO phonons.