  A $Z'$ boson associated with a broken $U(1)_{L_{\mu} - L_{\tau}}$ gauge
symmetry offers an economical solution to the long-standing $g_\mu-2$ anomaly,
confirmed and strengthened by recent measurements at Fermilab. Here, we revisit
the impact of such a $Z'$ on the spectrum of high-energy astrophysical
neutrinos, as measured by the IceCube experiment. This spectrum has been
observed to exhibit a dip-like feature at $E_{\nu} \sim 0.2-1 \, {\rm PeV}$,
which could plausibly arise from the physics of the sources themselves, but
could also be the consequence of high-energy neutrinos resonantly scattering
with the cosmic neutrino background, mediated by a $Z'$ with a mass on the
order of $m_{Z'} \sim 10 \, {\rm MeV}$. In this study, we calculate the impact
of such a $Z'$ on the high-energy neutrino spectrum for a variety of model
parameters and source distributions. For couplings that can resolve the
$g_{\mu}-2$ anomaly, we find that this model could self-consistently produce a
spectral feature that is consistent with IceCube's measurement, in particular
if the neutrinos observed by IceCube predominantly originate from high-redshift
sources.
