No. This is a widely circulated myth. However, there is no evidence to support the notion of self-reinfection via personal hygiene instruments while on or after hepatitis C treatment.
Taking this a step further, there isn’t much in the way of evidence showing that hepatitis C virus (HCV) can be transmitted on toothbrushes. Although experts recommend against sharing any personal hygiene objects that may have been used by someone with HCV, this advice is based on theory and commonsense rather than hard-core evidence. Theoretically, it makes sense to avoid any chance of contact with HCV.
However, this theory does not extend to reinfecting oneself with one’s own toothbrush or dentures. To date, there is no evidence of anyone being reinfected in this manner.