In liquid-liquid extraction systems, a large amount of water is dragged together with the extracted complexed ion into the receiving organic phase. The nature of this co-extracted water and its effect on the ion extraction selectivity are not well characterized. We report a series of molecular dynamics simulations on two chloroform-water binary mixtures, corresponding, respectively, to the saturation and supersaturation of water in chloroform. In the absence of solute, the most diluted solution contains only dimers of water, whereas in the most concentrated one, water aggregates in "droplets" of 5-9 and 9-12 H2O molecules. This contrasts with solutions containing the Na+ Pic(-) complexes of 1,3-alternate dimethorcycalix[4]arene-crown-6, where water aggregates around the Pic(-) counterion. The role of "dragged water" on the Na+/Cs+ extraction selectivity was investigated by MD-FEP studies in the two binary mixtures. We find that Cs+ is preferred, in agreement with experiment, but the selectivity decreases markedly as the humidity of the organic phase is increased. Based on these data we emphasize the role of the counterion on the water dragging to the organic phase and on the modulation of the ion extraction selectivity.