  We report a resonant inelastic X-ray scattering study on a single crystal of
a non-stoichiometric pyrochlore iridate Tb$_{2+x}$Ir$_{2-x}$O$_{7-y}$ ($x
\simeq 0.25$) that magnetically orders at $T_{\rm{N}}\simeq 50$ K. We find that
the strength of the spin-orbit coupling and the trigonal distortion of the
IrO$_6$ octahedra are comparable with the ones obtained in other pyrochlore
iridates. We observe a propagating gapped magnon mode at low energy, and model
it using a Hamiltonian consisting of a Heisenberg exchange [$J = 16.2(9)$ meV]
and Dzyaloshinskii-Moriya interactions [$D = 5.2(3)$ meV], which shows the
robustness of interactions despite Tb-stuffing at the Ir-site. Strikingly, the
ratio $D/J = 0.32(3)$ supports possible non-trivial topological magnon band
crossing. This material may thus host coexisting fermionic and bosonic
topology, with potential for manipulating electronic and magnonic topological
bands thanks to the $d-f$ interaction.
