  In this study, we explore the non-standard $\nu\bar{\nu}\gamma \gamma$
couplings parametrized by dimension-seven operators via $e^{+}e^{-} \to
\nu\bar{\nu}\gamma$ process at the FCC-ee/CEPC and
$\mu^{+}\mu^{-}\to\nu\bar{\nu}\gamma$ process at the Muon Colliders. For the
detailed Monte Carlo simulation, all signal and relevant background events are
produced within the framework of Madgraph where non-standard
$\nu\bar{\nu}\gamma \gamma$ couplings are implemented. After passing through
Pythia for parton showering and hadronization, detector effects are included
via tuned corresponding detector cards for each collider in Delphes. Projected
sensitivities on $\nu\bar{\nu}\gamma \gamma$ couplings are obtained at a
5$\sigma$ confidence level without and with $5\%$ systematic uncertainties for
the FCC-ee/CEPC and the Muon Colliders, showcasing the complementarity between
lepton colliders. Our best limit on the anomalous $\nu\bar{\nu}\gamma \gamma$
couplings even with 5\% systematic uncertainties for muon collider with
$\sqrt{s}=10$ TeV and $L_{int}=3$ ab$^{-1}$ are found to be thirteen orders of
magnitude stronger than the upper bound obtained from rare decay
$Z\to\gamma\gamma\nu\bar{\nu}$ analysis using LEP data.
