Monopole-fermion (and dyon-fermion) interactions provide a famous example
where scattering from a compact object gives a cross section much larger than
the object's geometrical size. This underlies the phenomenon of monopole
catalysis of baryon-number violation because the reaction rate is much larger
in the presence of a monopole than in its absence. It is sometimes claimed to
violate the otherwise generic requirement that short distance physics decouples
from long-distance observables -- a property that underpins the general utility
of effective field theory (EFT) methods. Decoupling in this context is most
simply expressed using point-particle effective field theories (PPEFTs)
designed to capture systematically how small but massive objects influence
their surroundings when probed only on length scales large compared to their
size. These have been tested in precision calculations of how nuclear
properties affect atomic energy levels for both ordinary and pionic atoms. We
adapt the PPEFT formalism to describe low-energy $S$-wave dyon-fermion
scattering with a view to understanding whether large catalysis cross sections
violate decoupling (and show why they do not). We also explore the related but
separate issue of the long-distance complications associated with polarizing
the fermion vacuum exterior to a dyon and show in some circumstances how PPEFT
methods can simplify calculations of low-energy fermion-dyon scattering in
their presence. We propose an effective Hamiltonian governing how dyon
excitations respond to fermion scattering in terms of a time-dependent vacuum
angle and outline open questions remaining in its microscopic derivation.