Many centralized matching markets are preceded by interviews between participants, including the residency matches between doctors and hospitals. Due to the COVID‐19 pandemic, interviews in the National Resident Matching Program were switched to a virtual format, which resulted in a dramatic and asymmetric decrease in the cost of accepting interview invitations. We study the impact of an increase in the number of doctors' interviews on their final matches. We show analytically that if doctors can accept more interviews, but hospitals do not increase the number of interviews they offer, then no doctor who would have matched in the setting with more limited interviews is better off and many doctors are potentially harmed. This adverse effect is the result of what we call interview hoarding. We characterize optimal mitigation strategies for special cases and use simulations to extend these insights to more general settings.