  We study scattering of a composite quasiparticle, which possesses a degree of
freedom corresponding to relative separation between two bound excitations, by
a delta-like impurity potential on a one-dimensional discrete lattice. Firstly,
we show that, due to specific properties of their dispersion, lattice
excitations bind to impurities with both negative and positive potentials. We
demonstrate that the finite size of the composite excitation leads to formation
of multiple excitation-impurity bound states. The number and the degree of
localization of these bound states depend on the signs and relative magnitudes
of the impurity potential and the binding strength of two quasiparticles. We
also report the existence of excitation-impurity bound states whose energies
are located in the continuum band. Secondly, we study a change in the
entanglement between the centre of mass and relative coordinate degrees of
freedom of a biexciton wave packet during single impurity scattering and
decoherence caused by it. For a composite quasiparticle on a lattice, the
entanglement between its relative and centre of mass coordinate degrees of
freedom arises naturally due to inseparability of the two-particle Hamiltonian.
One of the main focuses of our study is to investigate how this inseparability
affects the creation of the biexciton-impurity bound states and the
entanglement dynamics.
