The influence of the spin-Zeeman (SZ) operator in the evaluation of the spin-orbit effect on the nuclear magnetic shielding tensor in the context of the linear response within the elimination of the small component approach is critically discussed. It is shown that such term yields no contribution to the isotropic nuclear magnetic shielding constant, but it may be of great importance in the determination of individual tensor components, and particularly of the tensor anisotropy. In particular, an interesting relation between the SZ and orbital Zeeman contributions to the spin-orbit effect for the case of linear molecules is shown to hold. Numerical examples for the BrH, IH, and XeF(2) molecules are presented which show that, provided the SZ term is taken into account, results of the individual shielding tensor components and the tensor anisotropy are in good agreement with those obtained by other theoretical methods, and particularly by the Dirac-Hartree-Fock approach.