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Breaking of G-parity or new weak (second class) currents can be responsiblefor $\tau^- \to \eta^{(\prime)} \pi^- \nu_{\tau}$ decays. Forthcomingmeasurements of $\tau$ lepton properties at the Belle II experiment will beable to measure this decay channel for the first time. Isolating new physicscontributions from the measured rates will require a careful evaluation ofG-parity breaking contributions. Here we evaluate the one-loop contribution to$\tau^- \to \eta^{(\prime)} \pi^- \nu_{\tau}$ decays induced by the emission oftwo virtual photons and its later conversion into an $\eta^{(\prime)}$ meson.As expected, this contribution is very small and may be relevant only for newphysics searches contributing at the $10^{-4}$ level to the decay rate of$\tau^- \to \eta^{(\prime)} \pi^- \nu_{\tau}$ .

G-parity breaking in $\tau^- \to \eta^{(\prime)} \pi^- \nu_{\tau}$ decays induced by the $\eta^{(\prime)}\gamma\gamma$ form factor