We carefully analyse the contribution to the oscillations of a metallic gravitational antenna due to the interaction between the electrons of the bar and the incoming gravitational wave. To this end, we first derive the total microscopic Hamiltonian of the wave-antenna system and then compute the contribution to the attenuation factor due to the electron-graviton interaction. As compared to the ordinary damping factor, which is due to the electron viscosity, this term turns out to be totally negligible. This result confirms that the only relevant mechanism for the interaction of a gravitational wave with a metallic antenna is its direct coupling with the bar normal modes.