No, it is not possible to reverse a completion. Once someone has completed a program, they may not be unenrolled from that program and this action may not be undone.
As an administrator, we can remove the magic "complete" button from the staff view to avoid confusion.
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? :)