We perform a phenomenological study of the invariant mass distribution of hadronic jets produced in proton-proton collisions, in conjunction with a grooming algorithm. In particular, we consider the modified MassDrop Tagger (mMDT), which corresponds to Soft Drop with angular exponent β = 0. Our calculation, which is differential in both jet mass and jet transverse momentum, resums large logarithms of the jet mass, including the full dependence on the groomer's energy threshold z cut, and it is matched to fixed-order QCD matrix elements at next-to-leading order. In order to account for non-perturbative contributions, originating from the hadronisation process and from the underlying event, we also include a phenomenological correction factor derived from Monte Carlo parton shower simulations. Furthermore, we consider two different possibilities for the jet transverse momentum: before or after grooming. We show that the former should be preferred for comparisons with upcoming experimental data essentially because the mMDT transverse momentum spectrum is not collinear safe, though the latter exhibits less sensitivity to underlying event and displays properties that may provide complementary information for probing non-perturbative effects.