Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such settings, forming preferences is both difficult and critical. Prior work has suggested various prediction mechanisms that help agents make decisions about their preferences. Although often deployed together, these matching and prediction mechanisms are almost always analyzed separately. The present work shows that at the intersection of the two lies a previously unexplored type of strategic behavior: agents returning to the market (e.g., schools) can attack future predictions by interacting short-term non-optimally with their matches. Here, we first introduce this type of strategic behavior, which we call an adversarial interaction attack. Next, we construct a formal economic model that captures the feedback loop between prediction mechanisms designed to assist agents and the matching mechanism used to pair them. Finally, in a simplified setting, we prove that returning agents can benefit from using adversarial interaction attacks and gain progressively more as the trust in and accuracy of predictions increases. We also show that this attack increases inequality in the student population.