Click on the "Envelope Edit Tool" first? And then drag over the points to be removed.
It is not possible. In the Envelope Edit Tool, I cannot mark selected points with the mouse. Somehow I don't understand the function of the Envelope Edit Tool. It works just like the Normal edit Tool.
@pierre-k, it works on the last selected track only. And, yes, it apparently only works for selecting multiple points. But for a single point, just right-click and choose delete.
@pierre-k, no one's saying it can't be better. It just appeared you were overlooking the current possibilities that do let you delete multiple envelope nodes at once which your original video was indicating you could not.