  The power spectrum of reconstructed cosmic microwave background (CMB) lensing
maps is a powerful tool for constraints on cosmological parameters like the sum
of the neutrino masses and the dark energy equation of state. One possible
complication is the kinematic Sunyaev-Zel'dovich (kSZ) effect, due to the
scattering of CMB photons by moving electrons, which can bias the
reconstruction of the CMB lensing power spectrum through both kSZ-lensing
correlations and the non-Gaussianity of the kSZ temperature anisotropies. We
investigate for the first time the bias to CMB lensing reconstruction from
temperature anisotropies due to the reionization-induced kSZ signal and show
that it is negligible for both ongoing and upcoming experiments based on
current numerical simulations of reionization. We also revisit the bias induced
by the late-time kSZ field, using more recent kSZ simulations. We find that it
is potentially twice as large as found in earlier studies, reaching values as
large as several percent of the CMB lensing power spectrum signal, indicating
that this bias will have to be mitigated in upcoming data analyses.
