  The Universe's matter inhomogeneity gravitationally affects the propagation
of gravitational waves (GWs), causing the lensing effect. Particularly, the
weak lensing of GWs has been studied within the range of the Born approximation
to constrain the small-scale power spectrum. In this work, the validity of the
Born approximation is investigated by accounting for the higher-order terms in
the gravitational potential $\Phi$. To do so, we formulate the post-Born
approximation and derive the magnification $K$ and the phase modulation $S$ up
to third order in $\Phi$. We find that the average of $S$ and $K$ is non-zero
and that the average of $S$ depends on the size of the point mass. Due to this
size dependency, the signal is enhanced, and the number of GW events required
for detecting the average of $S$ decreases. We find that this number can become
comparable to or even smaller than the number required for detecting the
variance of $S$ in certain scenarios. In addition, it is verified that, for
lensing by dark low-mass halos, the post-Born corrections are a few orders of
magnitude smaller than the Born approximation at $f\geq0.01$~Hz. However, in
the presence of the point mass, there is a condition under which the Born
approximation fails. We derive the correction terms to the Born approximation
and identify the condition under which the Born approximation no longer holds.
For the magnification, the Born approximation is valid as long as the
wavelength of GWs is larger than the Schwarzschild radius of lenses, while for
the phase modulation, this condition is modified due to the physical size of
the point mass.
