  We extend the results of a previous paper where a model of interacting dark
energy, with a cosmological term decaying linearly with the Hubble parameter,
is tested against the observed mass power spectrum. In spite of the agreement
with observations of type Ia supernovas, baryonic acoustic oscillations and the
cosmic microwave background, we had shown previously that no good concordance
is achieved if we include the mass power spectrum. However, our analysis was
based on the ad hoc assumption that the interacting cosmological term is
strictly homogeneous. Now we perform a more complete analysis, by perturbing
such a term. Although our conclusions are still based on a particular, scale
invariant choice of the primordial spectrum of dark energy perturbations, we
show that a cosmological term decaying linearly with the Hubble parameter is
indeed disfavored as compared to the standard model.
