In dual tasks, with a visual-manual choice reaction time task in Task 1 and a go/no-go task in Task 2, not responding to Task 2 can have adverse effects on Task 1 performance, as demonstrated by no-go backward crosstalk effects (no-go BCE). Here, the response inhibition required to not respond to Task 2 spills over and slows response execution in Task 1. Over three experiments, we investigated whether the prospect of reward, which is a potent cognitive control modulator, influences no-go BCE. In Experiment 1, reward for fast and accurate responses in both tasks was modulated as a within-subject factor, and in Experiments 2 and 3, as a between-subject factor. The results revealed three major insights. In all three experiments, reward led to faster Task 1 and Task 2 performance. Second, despite this speeding, the no-go BCE was not modulated by reward. Finally, the reward led to more errors in Task 2 no-go trials. These results reveal a reward-induced bias for action, suggesting better preparedness to respond and, consequently, larger commission errors in Task 2 no-go trials. The absence of a reward-based modulation of the no-go BCE indicates that the reward-induced bias for action does not necessarily translate into larger response inhibition. These findings point towards the complex interactions between reward and inhibitory control and shed light on the potentials and limitations of reward-based modulation of dual-task interference.