Griffin, standing still. -1 to its attacks. 0 TMM.
Griffin, ground movement. +0 to its attacks. 2 TMM.
Griffin jumping. +2 to its attacks. 3 TMM.
Just noticed you referenced p16, which is in the intro rules. Looks like movement modes did not get added to the intro rules.
So without movement modes, the griffin is just +0 to its attacks, 3 TMM. Unless you couldn’t use jump jets (in water maybe), then it’s +0 to attacks, 2 TMM.