A fascinating type of symmetry-protected topological states of matter are topological Kondo insulators, where insulating behavior arises from Kondo screening of localized moments via conduction electrons, and nontrivial topology emerges from the structure of the hybridization between the local-moment and conduction bands. Here we study the physics of Kondo holes, i.e., missing local moments, in three-dimensional topological Kondo insulators, using a self-consistent real-space mean-field theory. Such Kondo holes quite generically induce in-gap states which, for Kondo holes at or near the surface, hybridize with the topological surface states. In particular, we study the surface-state quasiparticle interference (QPI) induced by a dilute concentration of surface Kondo holes and compare this to QPI from conventional potential scatterers. We treat both strong and weak topological-insulator phases and, for the latter, specifically discuss the contributions to QPI from inter-Dirac-cone scattering.