  We report an investigation of the lattice dynamical properties in a range of
Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ compounds, with special emphasis on the c-axis
polarized vibration of Fe with B$_{1g}$ symmetry, a Raman active mode common to
all families of Fe-based superconductors. We have carried out a systematic
study of the temperature dependence of this phonon mode as a function of Se $x$
and excess Fe $y$ concentrations. In parent compound Fe$_{1+y}$Te, we observe
an unconventional broadening of the phonon between room temperature and
magnetic ordering temperature $T_N$. The situation smoothly evolves towards a
regular anharmonic behavior as Te is substituted for Se and long range magnetic
order is replaced by superconductivity. Irrespective to Se contents, excess Fe
is shown to provide an additional damping channel for the B$_{1g}$ phonon at
low temperatures. We performed Density Functional Theory (DFT) ab-initio
calculations within the local density approximation (LDA) to calcuate the
phonon frequencies including magnetic polarization and Fe non-stoichiometry in
the Virtual Crystal Approximation (VCA). We obtained a good agreement with the
measured phonon frequencies in the Fe-deficient samples, while the effects of
Fe excess are poorly reproduced. This may be due to excess Fe-induced local
magnetism and low energy magnetic fluctuations that can not be treated
accurately within these approaches. As recently revealed by neutron scattering
and $\mu$-SR studies, these phenomena occur in the temperature range where
anomalous decay of the B$_{1g}$ phonon is observed, and suggests a peculiar
coupling of this mode with local moments and spin fluctuations in
Fe$_{1+y}$Te$_{1-x}$Se$_{x}$.
