Investigation of the inelastic neutron scattering spectra in Fe\(_{1+y}\)Te\(_{1-x}\)Se\(_{x}\) near a signature wave vector \(\mathbf{Q} = (1,0,0)\) for the bond-order wave (BOW) formation in parent compound Fe\(_{1+y}\)Te reveals an acoustic-phonon-like dispersion present in all structural phases. While a structural Bragg peak accompanies the mode in the low-temperature phase of Fe\(_{1+y}\)Te, it is absent in the high-temperature tetragonal phase, where Bragg scattering at this \(\mathbf{Q}\) is forbidden by symmetry. Notably, this mode is also observed in superconducting Fe\(_{1+y}\)Te\(_{1-x}\)Se\(_{x}\), where structural and magnetic transitions have been suppressed, and no BOW has been observed. The presence of this "forbidden" phonon indicates that the lattice symmetry is dynamically or locally broken by magnetic or orbital fluctuations, which are strongly coupled to the lattice degrees of freedom in these materials.