In a model of nonlocal 'transmission' of a finite amplitude plasma wave through a rectangular density barrier, the dependence of the intensity of the radiation regenerated in this ballistic effect on the barrier width is investigated in the case of a sufficiently long interaction of the incident wave with resonant particles. Both the collisionless case and that of weak collisions are examined. It is shown that for not too wide barriers the collisions may enhance the nonlocal transparency of the barrier.