Verin's Compulsion existed to work against the DO and for the side of the Light: it was to make her believe that Rand must be present for the Last Battle--this led her to swear fealty to Rand. Of course, that oath of fealty is no longer bound by the Oath Rod, but it at least provided an impetus for Elza to work with Rand, instead of against him.

Remember that we learned in tGS how difficult Compulsion is to remove. No doubt Semirhage had such a skill, as she knew how our bodies work better than anyone alive. Moridin realized Elza's Compulsion was a negative side effect, and so he sent Elza to someone who could surely remove it.