It is well known that Thomson scattering of CMB photons in galaxy clusters introduces new anisotropies in the CMB radiation field, but however little attention is payed to the fraction of CMB photons that are scattered off the line of sight, causing a slight blurring of the CMB anisotropies present at the moment of scattering. In this work we study this {it blurring} effect, and find that it has a non-negligible impact on estimations of the kinetic Sunyaev-Zeldovich (kSZ) effect: it induces a 10% correction in 20-40% of the clusters/groups, and a 100% correction in $sim 5$% of the clusters in an ideal (noiseless) experiment. We explore the possibility of using this blurring term to probe the CMB anisotropy field at different epochs in our Universe. In particular, we study the required precision in the removal of the kSZ that enables detecting the blurring term $-tau_T delta T / T_0$ in galaxy cluster populations placed at different redshift shells. By mapping this term in those shells, we would provide a tomographic probe for the growth of the Integrated Sachs Wolfe effect (ISW) during the late evolutionary stages of the Universe. We find that the required precision of the cluster peculiar velocity removal is of the order of 100 -- 200 km s$^{-1}$ in the redshift range 0.2 -- 0.8, after assuming that all clusters more massive than 10$^{14}$ h$^{-1}$ M$_{odot}$ are observable. These errors are comparable to the total expected linear line of sight velocity dispersion for clusters in WMAPV cosmogony, and correspond to a residual level of roughly 900 -- 1800 $tau_T mu$K per cluster, including all types of contaminants and systematics. Were this precision requirement achieved, then independent constraints on the intrinsic cosmological dipole would be simultaneously provided.
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