  Pion production is a significant component of the signal in accelerator-based
neutrino experiments. Over the last years, the MiniBooNE, T2K and MINERvA
collaborations have reported a substantial amount of data on
(anti)neutrino-induced pion production on the nucleus. However, a comprehensive
and consistent description of the whole data set is still missing. We aim at
improving the current understanding of neutrino-induced pion production on the
nucleus. To this end, the comparison of experimental data with theoretical
predictions, preferably based on microscopic models, is essential to
disentangle the different reaction mechanisms involved in the process. To
describe single-pion production (SPP) we use a hybrid model that combines a
low- and a high-energy approach. The low-energy model (LEM) contains resonances
and background terms. At high invariant masses, a high-energy model based on a
Regge approach is employed. The model is implemented in the nucleus using the
relativistic plane wave impulse approximation (RPWIA). We present a comparison
of the hybrid-RPWIA and LEM with the recent neutrino-induced charged current
$1\pi^+$ production cross section on water reported by T2K. In order to judge
the impact of final-state interactions (FSI) we confront our results with those
of the NuWro Monte Carlo generator. The hybrid-RPWIA model and NuWro compare
favorably to the data, albeit that FSI are not included in the former. These
results complement our previous work [Phys. Rev. D 97, 013004 (2018)] where we
compared the models to the MINERvA and MiniBooNE $1\pi^+$ data. The
hybrid-RPWIA model tends to overpredict both the T2K and MINERvA data in
kinematic regions where the largest suppression due to FSI is expected, and
agrees remarkably well with the data in other kinematic regions. On the
contrary, the MiniBooNE data is underpredicted over the whole kinematic range.
