  Cross-correlating the lensing signals of galaxies and comic microwave
background (CMB) fluctuations is expected to provide valuable cosmological
information. In particular it may help tighten constraints on parameters
describing the properties of intrinsically aligned galaxies at high redshift.
To access the information conveyed by the cross-correlation signal its accurate
theoretical description is required. We compute the bias to CMB lensing-galaxy
shape cross-correlation measurements induced by nonlinear structure growth.
Using tree-level perturbation theory for the large-scale structure bispectrum
we find that the bias is negative on most angular scales, therefore mimicking
the signal of intrinsic alignments. Combining Euclid-like galaxy lensing data
with a CMB experiment comparable to the Planck satellite mission the bias
becomes significant only on smallest scales ($\ell\gtrsim 2500$). For improved
CMB observations, however, the corrections amount to 10-15 per cent of the CMB
lensing-intrinsic alignment signal over a wide multipole range ($10 \lesssim
\ell \lesssim 2000$). Accordingly the power spectrum bias, if uncorrected,
translates into $2\sigma$ and $3\sigma$ errors in the determination of the
intrinsic alignment amplitude in case of CMB stage III and stage IV
experiments, respectively.
