For Fe-1, for the left-front atom we see that the 2 edges in the horizontal plane are 2 fold rotation axises, the axis indicated with the yellow pointer is 4-fold. Thus this yellow axis will be the z-axis of a PAS system and there is axial symmetry for the field gradient tensor.
For Fe-2, take the atom in the front plane, the 2 axisses in the horizontal plane are 2-fold, also the yellow pointer (moved a bit) is 2-fold, therefore our PAS is identified, however we do not have a 3 or more fold rotation axis, thus there is no axial symmetry
Seeing further lectures I’ve changed my mind:
for the Fe-2 atoms there is a 4-fold axis, pointing out of the plane of the cube, thus this will be the z-axis of the PAS
for the Fe-1 atoms there are multiple 4-fold axisses, thus the electric field gradient is 0