It is pointed that there is a current jump between the edge plasma inside the last closed magnetic surface and the scrape-off layer and the current jump can lead the external kink modes to convert to the tearing modes, due to the current interchange effects [L. J. Zheng and M. Furukawa, Phys. Plasmas 17, 052508 (2010)]. The magnetic reconnection in the presence of tearing modes subsequently causes the tokamak edge plasma to be peeled off to link to the diverters. In particular, the peeling or peeling-ballooning modes can become the "peeling-off" modes in this sense. This phenomenon indicates that the tokamak edge confinement can be worse than the expectation based on the conventional kink mode picture.