The Kassigs’ appeal is mostly based on an invocation of their son Abdul-Rahman Kassig’s humanitarian work among Syrians: they mention his conversion to Islam and refer to him by his Muslim name, but unlike the mother of another hostage, Shirley Sotloff, they do not presume to lecture the jihadis about Islam. The scarf that Mrs. Kassig is wearing over her head may be an oblique gesture of good will to the jihadis, but as much of her hair remains uncovered, it is unlikely to be regarded with anything but contempt.
The appeal to Abdul-Rahman Kassig’s humanitarian work is unlikely to move the jihadis. They don’t care about that at all. They only care about advancing Islam. If they decide that Abdul-Rahman Kassig’s severed head would serve Islam as a useful warning to the Infidels, then severed his head will be.