In this work, we analyze the scattering of light by the so-called spherulites or skyrmions in cholesteric liquid crystals. These are quasi-planar localized excitations of the director configuration. We compute the cross section of the polarization conversion for polarized incident light in the Born approximation, considering the anisotropic optical properties of the liquid crystal and the shape of the spherulite. We compare the results obtained by the analytical and the numerical skyrmion solutions found for several values of the model parameters. Finally, possible practical employments and theoretical extensions in the study of the phenomenon are foreseen.