Tunnelling of optical phonons across a quantum well is possible for a polar mode provided its frequency coincides with that of the two interface modes associated with the barrier. Because of this effect LO modes could scatter electrons in the well. In this paper we report a calculation of the total scattering rate caused by modes in the LO branch of the barrier material as a function of well width. We show that the form of the well-width dependence and the magnitude of the scattering rate is, to an excellent approximation, the same as that predicted by the dielectric continuum (DC) model, in which the scattering is caused by barrier interface modes obeying only electrical boundary conditions. This result provides, for the first time, justification for using Fuchs-Kliewer-like interface modes, even though these do not satisfy the necessary mechanical boundary conditions at the interfaces. It completes a study of the applicability of the DC model to the calculation of the scattering rates in a quantum well, a study that has already shown it to give a good agreement with the results of the hybrid model as regards the effects of modes in the well are concerned [2]. Our conclusion is that provided that the frequency-dependence of the coupling strength of the interface modes is correctly described, differences in detail concerning the effect of individual modes in the two models are unimportant for the total sum.