Pion production is one of the critical interaction systematic uncertainties in neutrino oscillation measurements. Recent GiBUU development has introduced many improvements in the treatment of pion production, including the $2\pi$ background in neutrino interactions. We present a comprehensive study of charge current neutrino-induced pion production with the GiBUU model by examining the processes contributing to pion production, including resonant, non-resonant, and background amplitudes, with a particular focus on the newly implemented $2\pi$ background. By comparing model predictions with experimental data from MINERvA, T2K, and MicroBooNE, we analyze the effects of in-medium modifications including NN cross modifications in $\Delta$ production and final-state interactions on observables such as transverse kinematic imbalance. The results show that these measurements can be adequately described with ad hoc combinations of model components, revealing the complexity and richness of the underlying nuclear dynamics.