We have demonstrated that the polarization of the fullerene shell considerably alters the polarization potential of an atom, stuffed inside a fullerene. This essentially affects the electron elastic scattering phases as well as corresponding cross sections. We illustrate the general trend by particular examples of electron scattering upon endohedrals Ne@C60 and Ar@C60. To obtain the presented results, we have suggested a simplified approach that permits to incorporate the effect of fullerenes polarizability into the Ne@C60 and Ar@C60 polarization potential. By applying this approach, we obtained numeric results that show strong variations in shape and magnitudes of scattering phases and cross sections due to effect of fullerene polarization upon the endohedral polarization potential.