  We employ inelastic helium atom-surface scattering to measure the low energy
phonon dispersion along high-symmetry directions on the surface of the
topological insulator Bi$_2$Te$_3$. Results indicate that one particular
low-frequency branch experiences noticeable mode softening attributable to the
interaction between Dirac fermion quasiparticles and phonons on the surface.
This mode softening constitutes a renormalization of the real part of the
phonon self-energy. We obtain the imaginary part, and hence lifetime
information, via a Hilbert transform. In doing so we are able to calculate an
average branch specific electron-phonon coupling constant $<\lambda_\nu> =
1.44$.
