Combined temperature-programmed desorption and IR studies suggest that absorption cross sections of IR-active vibrations of molecules strongly bound to single-wall carbon nanotubes (SWCNTs) are reduced at least by a factor of 10. Quantum chemical simulations show that IR intensities of endohedrally encapsulated molecules are dramatically reduced, and identify dielectric screening by highly polarizable SWCNT sidewalls as the origin of such screening. The observed intensity reduction originates from a sizable cancellation of adsorbate dipole moments by mirror charges dynamically induced on the nanotube sidewalls. For exohedrally adsorbed molecules, the dielectric screening is found to be orientation-dependent with a smaller magnitude for adsorption in groove and interstitial sites. The presented results clearly demonstrate and quantify the screening effect of SWCNTs and unequivocally show that IR spectroscopy cannot be applied in a straightforward manner to the study of peapod systems.