Raman scattering spectra of zigzag spin chain TaFe$_{1.25}$Te$_3$ single crystal are presented in a temperature range from 80 to 300 K. Nine Raman active modes of $A_g$ and $B_g$ symmetry are clearly observed and assigned by probing different scattering channels, which is confirmed by lattice dynamics calculations. Temperature dependence of the Raman modes linewidth is mainly governed by the lattice anharmonicity. The only deviation from the conventional behavior is observed for $A_g$ symmetry modes in a vicinity of the magnetic phase transition at $T_N approx 200$ K. This implies that the electron-phonon interaction weakly changes with temperature and magnetic ordering, whereas small changes in the spectra near the critical temperature can be ascribed to spin fluctuations.
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