  We present continuum and lattice calculations for elastic scattering between
a fermion and a bound dimer in the shallow binding limit. For the continuum
calculation we use the Skorniakov-Ter-Martirosian (STM) integral equation to
determine the scattering length and effective range parameter to high
precision. For the lattice calculation we use the finite-volume method of
L\"uscher. We take into account topological finite-volume corrections to the
dimer binding energy which depend on the momentum of the dimer. After
subtracting these effects, we find from the lattice calculation kappa a_fd =
1.174(9) and kappa r_fd = -0.029(13). These results agree well with the
continuum values kappa a_fd = 1.17907(1) and kappa r_fd = -0.0383(3) obtained
from the STM equation. We discuss applications to cold atomic Fermi gases,
deuteron-neutron scattering in the spin-quartet channel, and lattice
calculations of scattering for nuclei and hadronic molecules at finite volume.
