We have tested the hypothesis that for systems 24Mg + 90,92Zr, the shape of the barrier height distribution is not influenced by transfers processes. The experiment was performed using the ICARE detector system at the Warsaw Cyclotron. Having measured the transfer cross sections of the near-barrier collisions of 24Mg + 90,92Zr, we have found them to be roughly half of the value obtained for the 20Ne + 90,92Zr systems. From that observation, we conclude that in the 24Mg + 90,92Zr case, the leading cause of washing out the barrier distribution structure is the partial dissipation of relative kinetic energy into the non-collective excitation of the system.