  Spectroscopy of vortex bound states can provide valuable information on the
structure of the superconducting order parameter. Quasiparticle wavefunctions
are expected to leak out in the directions of gap minima or nodes, if they
exist, and scanning tunneling spectroscopy (STS) on these low-energy states
should probe the momentum dependence of the gap. Anisotropy can also arise from
band structure effects, however. We perform a quasiclassical calculation of the
density of states of a single vortex in an anisotropic superconductor, and show
that if the gap itself is not highly anisotropic, the Fermi surface anisotropy
dominates, preventing direct observation of superconducting gap features. This
serves as a cautionary message for the analysis of STS data on the vortex state
on Fe-based superconductors, in particular LiFeAs, which we treat explicitly.
