In Adam Glynn and Konstantin Kashin's study of the Job Training Partership Act (see causual diagram below), even though the mediator variable "Showed up" was affected by the confounder "Motivation", the researchers used the front-door criterion.

Through this study they showed that as long as the effect of the confounder (motivation) on the mediator (showed up) is relatively small, it can be treated as absent with minimal bias in the results