We investigate the scattering properties of the invisible lens in two ways. First, we describe the scattering of electromagnetic waves by the invisible lens realised by a purely dielectric, purely magnetic, and impedance-matched medium, respectively, using Debye potentials. Second, we employ the Wentzel–Kramers–Brillouin method to analyse the scattering of scalar waves by the lens. We show that in all cases the scattering is negligible for a discrete set of frequencies, while for other frequencies there is a phase slip at the boundary of the lens 'shadow'.