For the FeI atom:
It has three 4-fold rotation axes (x,y and z). All of these axes can be chosen as the z-axis of the PAS and eta = 0. (theorem 1)
Here, theormem 2 also states that the EFG tensor is zero.

For the FeII atom:
The z-axis is a 4-fold rotation axis and the x- and y- axes are 2-fold rotation axes. The z-axis can be chosen as the z-axis of the PAS and eta = 0. (theorem 1)
Here, theorem 2 doesn’t apply and so we cannot state that the EFG tensor will be zero.