  For the strongly correlated topological insulator SmB6 we discuss the
influence of a 2x1 reconstruction of the (001) surface on the topological
surface states. Depending on microscopic details, the reconstruction can be a
weak or a strong perturbation to the electronic states. While the former leads
to a weak backfolding of surface bands only, the latter can modify the
surface-state dispersion and lead to a Lifshitz transition. We analyze the
quasiparticle interference signal: while this tends to be weak in models for
SmB6 in the absence of surface reconstruction, we find that the 2x1
reconstruction can induce novel peaks. We discuss experimental implications.
