  We study the ground-state entanglement entropy of a subsystem of size $L$ of
non-interacting fermions scattered by a potential of finite range $a$. We
derive a general relation between the scattering matrix and the overlap matrix
and use it to prove, that for a one-dimensional symmetric potential the von
Neumann entropy, the R\'enyi entropies and the full counting statistics are
robust against potential scattering, provided that $L/a\gg 1$. The results of
numerical calculations support the validity of this conclusion for a generic
potential.
