  In a recent experiment [Trishin et al., Phys. Rev. Lett. 127, 236801 (2021)]
a rich physics was observed for Fe atoms on MoS$_2$/Au(111), characterized by
three different behaviors depending on the spectral density of the substrate
$\rho_c$: one dominated by a single ion anisotropy, one by the Kondo effect,
and an intermediate one. Based on symmetry and previous works, we show that the
appropriate model to describe the system is the anisotropic two-channel spin-1
Kondo model (A2CS1KM), which has an underlying topological quantum phase
transition (TQPT) between an ordinary Fermi liquid and a topological one with a
non-trivial value of the Luttinger integral. Solving the model with the
numerical renormalization group (NRG), we show that the different behaviors can
be explained in a unified fashion as a function of $\rho_c$, and correspond to
both Fermi liquids and an intermediate regime close to the TQPT in the
topological phase. Further experiments should confirm this transition.
