  We compute the dominant QED correction to the neutrino-electron interaction
rate in the vicinity of neutrino decoupling in the early universe, and estimate
its impact on the effective number of neutrino species $N_{\rm eff}$ in cosmic
microwave background anisotropy observations. We find that the correction to
the interaction rate is at the sub-percent level, consistent with a recent
estimate by Jackson and Laine. Relative to that work we include the electron
mass in our computations, but restrict our analysis to the enhanced $t$-channel
contributions. The fractional change in $N_{\rm eff}^{\rm SM}$ due to the rate
correction is of order $10^{-5}$ or below, i.e., about a factor of 30 smaller
than that recently claimed by Cielo {\it et al.}, and below the nominal
computational uncertainties of the current benchmark value of $N_{\rm eff}^{\rm
SM} = 3.0440 \pm 0.0002$. We therefore conclude that aforementioned number
remains to be the state-of-the-art benchmark for $N_{\rm eff}^{\rm SM}$ in the
standard model of particle physics.
