  We explore changes in the adiabatic low-order g-mode pulsation periods of
0.526, 0.560, and 0.729 M$_\odot$ carbon-oxygen white dwarf models with
helium-dominated envelopes due to the presence, absence, and enhancement of
$^{22}$Ne in the interior. The observed g-mode pulsation periods of such white
dwarfs are typically given to 6$-$7 significant figures of precision. Usually
white dwarf models without $^{22}$Ne are fit to the observed periods and other
properties. The root-mean-square residuals to the $\simeq$ 150$-$400 s
low-order g-mode periods are typically in the range of $\sigma_{rms}$
$\lesssim$ 0.3 s, for a fit precision of $\sigma_{rms}/ P$ $\lesssim$ 0.3 %. We
find average relative period shifts of $\Delta P/P$ $\simeq$ $\pm$ 0.5 % for
the low-order dipole and quadrupole g-mode pulsations within the observed
effective temperature window, with the range of $\Delta P/P$ depending on the
specific g-mode, abundance of $^{22}$Ne, effective temperature, and mass of the
white dwarf model. This finding suggests a systematic offset may be present in
the fitting process of specific white dwarfs when $^{22}$Ne is absent. As part
of the fitting processes involves adjusting the composition profiles of a white
dwarf model, our study on the impact of $^{22}$Ne can provide new inferences on
the derived interior mass fraction profiles. We encourage routinely including
$^{22}$Ne mass fraction profiles, informed by stellar evolution models, to
future generations of white dwarf model fitting processes.
