Doesn't it depend upon how many people you are referring to? The first seems to be for more than one member of staff and the second could be changed to 'A staff member who has previously undertaken ...'.
'Staff who have' is correct.
It may have been 'greenlined' because a staff (as in pole) is a singular item and staff can be a singular collective term (he is part of our staff).
If in doubt change it to 'members of staff' or 'employees'