  Hu [Phys. Rev. D62 (2000) 043007] has presented a harmonic-space method for
calculating the effects of weak gravitational lensing on the cosmic microwave
background (CMB) over the full sky. Computing the lensed power spectra to first
order in the deflection power requires one to formulate the lensing
displacement beyond the tangent-space approximation. We point out that for CMB
polarization this displacement must undergo geometric corrections on the
spherical sky to maintain statistical isotropy of the lensed fields. Although
not discussed by Hu, these geometric effects are implicit in his analysis.
However, there they are hidden by an overly-compact notation that is both
unconventional and rather confusing. Here we aim to ameliorate this deficiency
by providing a rigorous derivation of the lensed spherical power spectra.
