What the parent means is that in the Tasmanian devils' case it's the cancerous cells of another animal which are transmitted, not some kind of virus or similar

What the parent means is that in the Tasmanian devils' case it's the cancerous cells of another animal which are transmitted, not some kind of virus or similar that introduces genetic damage in the host. Since the improved/strengthened cell death mechanism introduced by the therapy would only affect your own cells (as the introduced cells wouldn't have the altered genes), there would be no change to the cancerousness of the transmitted cells.