  In this paper we show how the rescattering of CMB photons after cosmic reionization can give a significant linear contribution to the temperature-matter cross-correlation measurements. These anisotropies, which arise via a late time Doppler effect, are on scales much larger than the typical scale of non-linear effects at reionization; they can contribute to degree scale cross-correlations and could affect the interpretation of similar correlations resulting from the integrated Sachs-Wolfe effect. While expected to be small at low redshifts, these correlations can be large given a probe of the density at high redshift, and so could be a useful probe of the cosmic reionization history. 
The effect of reionization on the CMB-density correlation