What should a person do who led the prayer while being in a state of ritual impurity (حدث), then remembered this during the prayer and completed it?

Completing the prayer with people after realizing one is in a state of ritual impurity (hadath) is an error and requires repentance. The obligation was to withdraw from the prayer upon realizing the hadath and appoint someone else to complete the prayer. It is not necessary to inform the people of what happened, and there is no betrayal in not informing them, because their prayer is valid as long as they are unaware of their Imam's state of impurity.