In previous works it has been shown that the Debye-Waller (DW) exponent for Helium atom specular reflection from a conducting surface, when measured as a function of temperature in the linear high-temperature regime, allows for the determination of the surface electron-phonon coupling. However, there exist a number of experimental measurements that exhibit non-linearities in the DW exponent as a function of the surface temperature. Such non-linearities have been suggested as due to vibrational anharmonicity or a temperature dependence of the surface carrier concentration. In this work, it is suggested, on the basis of a few recent experimental data, that the deviations from linearity of the DW exponent temperature-dependence, as observed for conducting surfaces or supported metal overlayers with the present high-resolution He-atom scattering, permit to single out the specific role of high-energy phonons in the surface electron-phonon mass-enhancement factor.