We demonstrate that the differential conductance, dI/dV, measured via spectroscopic imaging scanning tunneling microscopy in the doped iron chalcogenide FeSe0.45Te0.55, possesses a series of characteristic features that allow one to extract the orbital structure of the superconducting gaps. This yields nearly isotropic superconducting gaps on the two holelike Fermi surfaces, and a strongly anisotropic gap on the electronlike Fermi surface. Moreover, we show that the pinning of nematic fluctuations by defects can give rise to a dumbbell-like spatial structure of the induced impurity bound states, and explains the related C2 symmetry in the Fourier transformed differential conductance. © 2017 American Physical Society.