  Unresolved coalescing binary neutron stars in the Galaxy and beyond produce a
stochastic gravitational wave background within the LISA frequency band, which
can be potentially dangerous for possible detection of fundamentally more
interesting relic cosmological backgrounds. Here we address the question what
effects the unavoidable eccentricity of orbits of these systems should have on
the properties of this backgrounds. In particularly, we examine starting from
which frequency one-year observations with LISA can be secure from
contamination by the noise produced by galactic binary neutron stars in
eccentric orbits. We come to the conclusion that harmonics from such binaries
do not contribute significantly above $\sim 10^{-3}$ Hz.
