We present a magneto-optical study of the three-dimensional topological insulator, strained HgTe, using a technique which capitalizes on advantages of time-domain spectroscopy to amplify the signal from the surface states. This measurement delivers valuable and precise information regarding the surface-state dispersion within <1  meV of the Fermi level. The technique is highly suitable for the pursuit of the topological magnetoelectric effect and axion electrodynamics.