No, it is not possible to reverse a completion. Once someone has completed a program, they may not be un-enrolled from that program and this action can not be undone.
To avoid confusion among your staff, you can ask the Beanstack team to remove the magic "complete" button from the staff view.
In the case of an accidental completion, you will want to consider deleting the reader, and then re-adding them and bulk logging whatever they had accomplished all at one time for them.
Did we mention this action cannot be reversed? :)