Cotunneling into Kondo systems, where an electron enters an f-electron material via a cotunneling process through the local-moment orbital, has been proposed to explain the characteristic line shapes observed in scanning-tunneling-spectroscopy (STS) experiments. Here we extend the theory of electron cotunneling to Kondo-lattice systems in which the bulk hybridization between conduction and f electrons is odd under inversion, being particularly relevant to Kondo insulators. Compared to the case of even hybridization, we show that the interference between normal tunneling and cotunneling processes is fundamentally altered: it is entirely absent for layered, i.e., quasi-two-dimensional materials, while its energy dependence is strongly modified for three-dimensional materials. We discuss implications for STS experiments.