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In recent years, transition metal dichalcogenides (TMDs) have garnered great interest as topological materials. In particular, monolayers of centrosymmetric -phase TMDs have been identified as 2D topological insulators (TIs), and bulk crystals of noncentrosymmetric -phase and have been identified as type-II Weyl semimetals. However, angle-resolved photoemission spectroscopy and STM probes of these semimetals have revealed huge, arclike surface states that overwhelm, and are sometimes mistaken for, the much smaller topological surface Fermi arcs of bulk type-II Weyl points. In this Letter, we calculate the bulk and surface electronic structure of both - and -. We find that - is, in fact, a -nontrivial higher-order TI (HOTI) driven by double band inversion and exhibits the same surface features as - and -. We discover that these surface states are not topologically trivial, as previously characterized by the research that differentiated them …