These interaction channels are mainly relevant at low energies due to their energy threshold, which is much lower than that of equivalent interactions on carbon-12.

However, carbon-13 makes up only about 1% of carbon nuclei in nature. Thus, even at low energies I’d estimate that the event rate of these interactions is about an order of magnitude smaller than that of neutrino-electron scattering. That would make this a very minor correction.

A theoretical calculation (including a nice numerical fit) of the cross-section is available.