  The electronic structure of a vortex pinned by an insulating columnar
inclusion in a type-II chiral $p_x \pm i p_y$ superconductor is studied within
the Bogolubov-de Gennes theory. The structure of the anomalous spectral branch
is shown to be strongly affected by the mutual orientations of the angular
momenta of the center of mass and the relative motion of the two electrons in
the Cooper pair. Being only slightly perturbed by the scattering at the defect
for the zero sum of these angular momenta the anomalous spectral branch appears
to change dramatically in the absence of such compensation. In the latter case
the defect presence changes the anomalous branch slope sign at the Fermi level
resulting in the quasiparticle angular momenta inversion at the positive
energies and the impact parameters smaller than the defect radius. The
experimentally observed consequences for the scanning tunneling microscopy
characteristics and vortex dynamics are discussed.
