We consider scattering of a single particle from an interaction-bound pair of particles in the one-dimensional Bose-Hubbard model. We show that the transmission probability of the single particle is always significantly smaller than unity. This invalidates the main result of L. Jin et al. [Phys. Rev. A 79, 032108 (2009)], where it is claimed that a single-particle wave packet can pass with unit probability through a bound-particle pair and coherently shift its position by one lattice site.