If an employee is classified as nonexempt from overtime but actually should receive overtime, then any overtime they have worked you must pay them and the associated taxes. The courts will enforce this.
It’s important to always keep clear records of hours worked by all employees. If you were paying overtime and they were really exempt you have a different problem. You paid them overtime wages they were not due. Trying to get that back is going to be difficult internally with a very upset worker and may be impossible to enforce if the employee objects.