  Binary neutron stars mergers widely accepted as potential progenitors of
short gamma-ray bursts. After the remnant of the merger has collapsed to a
black hole, a jet is powered and may breakout from the the matter expelled
during the collision and the subsequent wind emission. The interaction of the
jet with the ejecta may affect its dynamics and the resulting electromagnetic
counterparts. We here examine how an inhomogeneous and anisotropic distribution
of ejecta affects such dynamics, dictating the properties of the jet-ejecta
cocoon and of the afterglow radiated by the jet upon deceleration. More
specifically, we carry out general-relativistic hydrodynamical simulations of
relativistic jets launched within a variety of geometrically inhomogeneous and
anisotropic distributions of ejected matter. We find that different
anisotropies impact the variance of the afterglow light-curves as a function of
the jet luminosity and ejected mass. A considerable amount of the jet energy is
deposited in the cocoon through the jet-ejecta interaction with a small but
important dependence on the properties of the ejecta. Furthermore, all
configurations show a two-component behaviour for the polar structure of the
jet, with a narrow core at large energies and Lorentz factors and a shallow
segment at high latitudes from the jet axis. Hence, afterglows measured on
off-axis lines of sight could be used to deduce the properties of the ejected
matter, but also that the latter need to be properly accounted for when
modelling the afterglow signal and the jet-launching mechanisms.
