  A hole in a two-dimensional Ising antiferromagnet was believed to be
infinitely heavy due to the string of wrongly oriented spins it creates as it
moves, which should trap it near its original location. Trugman showed that, in
fact, the hole acquires a finite effective mass due to contributions from
so-called {\it Trugman loop} processes, where the hole goes nearly twice around
closed loops, first creating and then removing wrongly-oriented spins, and
ending up at a different lattice site. This generates effective second- and
third-nearest-neighbor hopping terms which keep the quasiparticle on the
sublattice it was created on. Here, we investigate the trapping of the
quasiparticle near a single attractive non-magnetic impurity placed at one
lattice site. We consider the two cases with the quasiparticle and impurity
being on the same versus on different sublattices. The main result is that even
though the quasiparticle can not see the bare disorder in the latter case, the
coupling to magnons generates an effective renormalized disorder on its own
sublattice which is strong enough to lead to bound states, which however have a
very different spectrum than when the quasiparticle and impurity are on the
same sublattice.
