The phenomenon of wave polarization conversion occurs when an electromagnetic wave of elliptical polarization is incident upon a layered structure comprising a strip grating, magnetodielectric layer, chiral layer, and screen. For suitable choice of structural parameters, we discovered regimes where the specularly reflected wave is nearly totally transformed into a linearly polarized wave. Due to the presence of a chiral medium, the corresponding diffraction problem is an intrinsically vectorial problem. It is solved using an analytical regularization procedure based on the Riemann-Hilbert problem method and the obtained solution thus admits an effective numerical treatment. It is shown that a nearly total polarization transformation can be realized for different elliptical polarisation parameters of the incident wave over a rather wide range of incident wave angles. The exhibition of polarization transformation is affected by the resonance properties of the grating-screen volume and by the grating. The purity of polarization conversion may be effectively controlled by careful choice of the structure parameters.