Telescopes measuring cosmic microwave background (CMB) polarization on large angular scales require exquisite control of systematic errors to ensure the fidelity of the cosmological results. In particular, far-sidelobe contamination from wide angle scattering is a potentially prominent source of systematic error for large aperture microwave telescopes. Here we describe and demonstrate a ray-tracing-based modeling technique to predict far sidelobes for a three mirror anastigmat telescope designed to observe the CMB from the South Pole. Those sidelobes are produced by light scattered in the receiver optics subsequently interacting with the walls of the surrounding telescope enclosure. After comparing simulated sidelobe maps and angular power spectra for different enclosure wall treatments, we propose a highly scattering surface that would provide more than an order of magnitude reduction in the degree-scale far-sidelobe contrast compared to a typical reflective surface. We conclude by discussing the fabrication of a prototype scattering wall panel and presenting measurements of its angular scattering profile.