B-mode CMB polarization from patchy screening during reionization

B modes in CMB polarization from patchy reionization arise from two effects: generation of polarization from scattering of quadrupole moments by reionization bubbles and fluctuations in the screening of E modes from recombination. The scattering contribution has been studied previously, but the screening contribution has not yet been calculated. We show that on scales smaller than the acoustic scale (l > or approx. 300), the B-mode power from screening is larger than the B-mode power from scattering. The ratio approaches a constant ∼2.5 below the damping scale (l > or approx. 2000). On degree scales relevant for gravitational waves (l < or approx. 100), screening B modes have a white noise tail and are subdominant to the scattering effect. These results are robust to uncertainties in the modeling of patchy reionization.