We use model five-level systems to study resonance leaking of pi-pulse-induced multiphoton (MP) transitions along a strongly coupled anharmonic ladder. We demonstrate that the presence of a weakly bound background state attached to the ladder either in linear or Lambda configuration can have very pronounced effects on resonant MP ladder transitions, including essentially complete quenching of the primary transition. We also develop control strategies for the elimination of background state population based on phase-adjusted Gaussian pulse pairs and discuss the underlying control mechanisms. Finally we show that these strategies are effective in realistic molecular many-level systems. In particular, we demonstrate efficient pulse-pair control of resonance leaking in a 165-level system modeling vibrational excitation in HCN.