  Observed CMB anisotropies are lensed, and the lensed power spectra can be
calculated accurately assuming the lensing deflections are Gaussian. However,
the lensing deflections are actually slightly non-Gaussian due to both
non-linear large-scale structure growth and post-Born corrections. We calculate
the leading correction to the lensed CMB power spectra from the
non-Gaussianity, which is determined by the lensing bispectrum. The
lowest-order result gives $\sim 0.3\%$ corrections to the BB and EE
polarization spectra on small-scales, however we show that the effect on EE is
reduced by about a factor of two by higher-order Gaussian lensing smoothing,
rendering the total effect safely negligible for the foreseeable future. We
give a simple analytic model for the signal expected from skewness of the
large-scale lensing field; the effect is similar to a net demagnification and
hence a small change in acoustic scale (and therefore out of phase with the
dominant lensing smoothing that predominantly affects the peaks and troughs of
the power spectrum).
