SmB6 is one of the candidate compounds for topological Kondo insulators, a class of materials which combines a nontrivial topological band structure with strong electronic correlations. Here we employ a multiband tight-binding description, supplemented by a slave-particle approach to account for strong interactions, to theoretically study the surface-state signatures in scanning tunneling spectroscopy and quasiparticle interference (QPI). We discuss the spin structure of the three surface Dirac cones of SmB6 and provide concrete predictions for the energy and momentum dependence of the resulting QPI signal. Our results also apply to PuB6, a strongly correlated topological insulator with a very similar electronic structure.