Adversarial attacks on learning-based multi-modal trajectory predictors have already been demonstrated. However, there are still open questions about the effects of perturbations on inputs other than state histories, and how these attacks impact downstream planning and control. In this paper, we conduct a sensitivity analysis on two trajectory prediction models, Trajectron++ and AgentFormer. The analysis reveals that between all inputs, almost all of the perturbation sensitivities for both models lie only within the most recent position and velocity states. We additionally demonstrate that, despite dominant sensitivity on state history perturbations, an undetectable image map perturbation made with the Fast Gradient Sign Method can induce large prediction error increases in both models, revealing that these trajectory predictors are, in fact, susceptible to image-based attacks. Using an optimization-based planner and example perturbations crafted from sensitivity results, we show how these attacks can cause a vehicle to come to a sudden stop from moderate driving speeds.