The appearance of corotating Keplerian discs orbiting Kerr superspinars has been shown to be strongly dependent on the value of the superspinar spin in both their shape and frequency shift profile, demonstrating clear distinctions from the corotating discs around black holes. However, it has to be modified in the innermost parts of the disc by the self-illumination effect caused by the photons trapped in the strong gravitational field near the superspinars with spin a < 9. Here we demonstrate that self-illumination is irrelevant for counter-rotating Keplerian discs orbiting in the field of all Kerr superspinars since such discs are located at the regions where none of the radiated photons can be trapped. Therefore, the results obtained by considering the escaping photons only are quite relevant for the appearance of the counter-rotating Keplerian discs orbiting Kerr superspinars. The appearance and spectral continuum of such discs differ from those of counter-rotating discs in the field of Kerr black holes. The differences are of quantitative character except the existence of the disc images located inside the image of the inner edge of the disc that are created by photons reaching regions close to the surface of Kerr superspinars. Their observational relevance is realistic in the near future for accretion phenomena in the vicinity of Sgr A*.