After retrieval, reactivated memories may destabilize and require restabilization processes to persist, referred to as reconsolidation. The reminder-extinction procedure has been proposed as a behavioral reconsolidation-based intervention to persistently attenuate threat-conditioned memories. After the presentation of a single reminder trial, the conditioned threat memory may enter a labile state, and extinction training during this window can prevent the return of conditioned threat responses. However, findings on this reminder-extinction procedure are mixed and its effectiveness may be subject to boundary conditions, including memory strength. Here, we systematically investigate whether more intense threat memories are less susceptible to disruption through a reminder-extinction procedure. Using a Pavlovian auditory threat conditioning procedure at three different shock intensities, rats acquired conditioned threat responses of variable "strength." Rats subsequently underwent either extinction preceded by a reminder or standard extinction. Although different shock intensities led to different strength threat memories, all groups showed reinstatement of conditioned threat responses irrespective of shock intensity or reminder condition. Hence, regardless of the intensity of the threat memory, the reminder procedure was ineffective in preventing the return of threat responses in rats. We thus find no evidence that threat memory intensity is a potential modulator of the effectiveness of the reminder-extinction procedure.