The impact of surface heterogeneity on the IR spectroscopy of the CO stretching vibration is explored through vibrational line profile synthesis. The impact of surface heterogeneity is revealed through the application of the pre-exponential optimised inversion method of Smith et al. (2016) to previously reported sub-monolayer thermal desorption studies of carbon monoxide desorption from an amorphous silica surface [Taj et al. (2017, 2019a)]. Comparison is made to this previous investigation of CO line profiles on this surface and on amorphous solid water. A tentative conclusion is drawn that CO vibrationally-promoted desorption from, and diffusion on, the amorphous silica surface may be responsible for the correspondingly short vibrational excited state lifetime on that surface. The contrast with CO on amorphous solid water, where direct and rapid vibrational relaxation into the solid water phonon bath occurs, is highlighted. The consequences of this from the standpoint of CO deposition on grain surfaces are discussed.