  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 of parent compound
Fe$_{1+y}$Te [Phys. Rev. Lett. 112, 187202 (2014)] 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 FeTe$_{0.55}$Se$_{0.45}$, where
structural and magnetic transitions are suppressed, and no BOW has been
observed. The presence of this "forbidden" phonon indicates that the lattice
symmetry is dynamically or locally broken by magneto-orbital BOW fluctuations,
which are strongly coupled to lattice in these materials.
