  The flux of electron and positron cosmic rays measured by the space-based
experiments PAMELA, AMS-02, CALET, DAMPE and Fermi-LAT shows an unexpected
behaviour at high energies, in comparison with expectations from standard
astrophysical sources. In particular, AMS-02 observations provide compelling
evidence for a new source of positrons and electrons whose origin is still
unknown. Plausible scenarios include either the contribution of dark matter or
unresolved astrophysical sources, such as nearby pulsars. It has been shown
that explanations based mostly on dark matter, tend to overproduce gamma-rays,
entering in conflict with measurements of the extra-galactic gamma-ray
background (EGB). Although this situation seems to be quite generic, it
ultimately depends on the properties of the dark matter candidate. In this work
we revisit a model in which the gravitino is a dark matter candidate decaying
to SM particles through R-parity violating couplings. We show that decay
channels allowed by trilinear couplings produce more electrons and positrons
and fewer photons in comparison to channels allowed by bilinear couplings.
Indeed, when considering AMS-02 data alone we find that the trilinear model is
compatible with EGB constraints. However, this result may change when DAMPE or
CALET measurements of the sum of electrons and positrons fluxes are considered
instead of AMS-02 data. Therefore, in order to evaluate this model further,
discrepancies between the data collected by these experiments need to be
clarified
