  We introduce here a cross-correlation term between CMB lensing and galaxy
intrinsic alignment, noted hereby as $\phi I$. This effect acts as a
contaminant to the cross-correlation between CMB lensing and galaxy lensing.
The latter cross-correlation has recently been detected for the first time, and
measurements will greatly improve as the area of overlap between galaxy and CMB
surveys increases and measurements of the CMB polarization become more
significant. This will constitute a powerful probe for studying the structure
and evolution of the universe. The magnitude of the $\phi I$ term is found to
be about 15% of the pure CMB lensing-galaxy lensing component and acts to
reduce the magnitude of its measured spectrum. This offset in the spectrum will
strongly impact its use for precision cosmological study if left unmitigated.
We also propose here a method to calibrate this $\phi I$ contamination through
use of a scaling relation that allows one to reduce the impact of $\phi I$ by a
factor of 20 or more in all redshift bins, which would reduce its magnitude
down to detection limits in almost all cases. This will allow the full use of
this probe for precision cosmology.
