  We study analytically and with the numerical time-evolving block decimation
method the dynamics of an impurity in a bath of spinless fermions with
nearest-neighbor interactions in a one-dimensional lattice. The bath is in a
Mott insulator state with alternating sites occupied and the impurity interacts
with the bath by repulsive on-site interactions. We find that when the
magnitudes of the on-site and nearest-neighbor interactions are close to each
other, the system shows excitations of two qualitatively distinct types. For
the first type, a domain wall and an anti-domain wall of density propagate in
opposite directions, while the impurity stays at the initial position. For the
second one, the impurity is bound to the anti-domain wall while the domain wall
propagates, an excitation where the impurity and bath are closely coupled.
