  Compensated isocurvature perturbations (CIPs) are modes in which the baryon
and dark matter density fluctuations cancel. They arise in the curvaton
scenario as well as some models of baryogenesis. While they leave no observable
effects on the cosmic microwave background (CMB) at linear order, they do
spatially modulate two-point CMB statistics and can be reconstructed in a
manner similar to gravitational lensing. Due to the similarity between the
effects of CMB lensing and CIPs, lensing contributes nearly Gaussian random
noise to the CIP estimator that approximately doubles the reconstruction noise
power. Additionally, the cross correlation between lensing and the integrated
Sachs-Wolfe (ISW) effect generates a correlation between the CIP estimator and
the temperature field even in the absence of a correlated CIP signal. For
cosmic-variance limited temperature measurements out to multipoles $l \leq
2500$, subtracting a fixed lensing bias degrades the detection threshold for
CIPs by a factor of $1.3$, whether or not they are correlated with the
adiabatic mode.
