We present a low temperature scanning tunneling spectroscopy (STS) study of the superconducting properties of monolayers of FeSe0.5Te0.5 grown on the three-dimensional (3D) topological insulator Bi2Se1.2Te1.8. While the morphology and the overall transition temperature resembles those of similarly doped bulk crystals, we find a two-fold anisotropic s-wave gap function. The two-fold nature of the gap symmetry is evident from the Bogoliubov quasiparticle interference (QPI) pattern, which shows distinct C-2 symmetric scattering intensities. Spatially resolved spectroscopic data shows a strong inhomogeneity in the size and anisotropy strength of the energy gaps, which cannot be correlated merely to the local chemical disorder. Instead, we argue that the gap inhomogeneity emerges with a similar mechanism as in disordered superconductors. Our sample system provides an ideal platform to study unconventional superconductivity in close proximity to a topological insulator.