For the strongly correlated topological insulator SmB₆ we discuss the influence of a 2×1 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 the surface bands only, the latter can modify the surface-state dispersion and lead to a Lifshitz transition.Weanalyze the quasiparticle interference signal: while this tends to be weak in models for SmB₆ in the absence of surface reconstruction, we find that the 2×1 reconstruction can induce novel peaks.Wediscuss experimental implications.