  Jet quenching in heavy ion collisions is expected to be accompanied by recoil
effects, but unambiguous signals for the induced medium response have been
difficult to identify so far. Here, we argue that modern jet substructure
measurements can improve this situation qualitatively since they are sensitive
to the momentum distribution inside the jet. We show that the groomed subjet
shared momentum fraction $z_g$, and the girth of leading and subleading subjets
signal recoil effects with dependencies that are absent in a recoilless
baseline. We find that recoil effects can explain most of the medium
modifications to the $z_g$ distribution observed in data. Furthermore, for jets
passing the Soft Drop Condition, recoil effects induce in the differential
distribution of subjet separation $\Delta R_{12}$ a characteristic increase
with $\Delta R_{12}$, and they introduce a characteristic enhancement of the
girth of the subleading subjet with decreasing $z_g$. We explain why these
qualitatively novel features, that we establish in \textsc{Jewel+Pythia}
simulations, reflect generic physical properties of recoil effects that should
therefore be searched for as telltale signatures of jet-induced medium
response.
