Suppression of current in the ground plane
Your title asks for suppression in the ground place. That makes no sense,  the field around the stripline induces current in the ground plane, otherwise it wouldn't be a stripline (but a free-hanging wire antenna).
I'm hence interpreting you like you think that relatively far away from one strip line, there's field caused by it that interacts with the other stripline. That might be, but that mostly means your ground isn't sufficient conductive (i.e. more current directly below/above the stripline is the solution), or you've really, really put the two striplines too close together.