> Then fire them. <
Right you are. And perhaps also consider a criminal investigation, to see if any overpayments were deliberate.
But no one gets fired from a government job anymore. Or should I say, permanently fired. Many folks who do get fired, appeal. They win their appeal and get their jobs back. With back pay, of course.
This not only keeps bad workers in their jobs. It also demoralizes the good workers.
Firing a fed govt employee is an automatic black mark on his supervisor. The official govt stance is that there are no bad employees. Yes, this is insane. But that is the system. The few decent people in govt are hamstrung by masses of insane regulations.