Fe 1: The vertical direction is a 2-fold rotation since the horizontal plane lattice parameters differ, this is the same scenario as for one the horizontal directions. However the other horizontal has the same lattice parameters and thus gives a 4-fold rotation. This means choosing the z-axis to be this final axis provides us with axial symmetry (eta=0) but the EFG tensor is not zero since we only have one 3-fold or more rotation.
Fe 2: Considerring the green iron atoms we obtain a similar situation which results in the same rotations. This means we again have axial symmetry if we choose the same z-axis as before end the EFG tensor is nonzero.
In general this means the crystal can be described axially symmetric but the EFG can’t be set to zero.