The intent of the "under the terms of this License" clause here is to require the conveyed "Corresponding Source" to be GPLv3 licensed as well. On a lay readin

The intent of the "under the terms of this License" clause here is to require the conveyed "Corresponding Source" to be GPLv3 licensed as well. On a lay reading, this could also be interpreted as "in the manner specified by this license". Whether that's how the courts would understand it is a question for a lawyer. It may hinge on what, specifically, was originally licensed under the GPL: the source code or the binary artifacts.