Bilinear $R$-parity violation provides an attractive origin for neutrino masses and mixings. In such schemes the gravitino is a viable decaying dark matter particle whose $R$-parity violating decays lead to monochromatic photons with rates accessible to astrophysical observations. We determine the parameter region allowed by gamma-ray line searches, dark matter relic abundance, and neutrino oscillation data, obtaining a limit on the gravitino mass ${m}_{\stackrel{\texttildelow{}}{G}}\ensuremath{\lesssim}1--10\text{ }\text{ }\mathrm{GeV}$ corresponding to a relatively low reheat temperature ${T}_{R}\ensuremath{\lesssim}\mathrm{\text{few}}\ifmmode\times\else\texttimes\fi{}{10}^{7}--{10}^{8}\text{ }\text{ }\mathrm{GeV}$. Neutrino mass and mixing parameters may be reconstructed at accelerator experiments like the Large Hadron Collider.