When we started working with the change parry it was in response to the beat attack. If an opponent beats your blade you can:
... control distance, make the attack fall short, and take over the action, or
... immediately counterattack (in epee and possibly in sabre if you can control distance), or
... make a beat parry on the extending blade, or
... change parry and riposte.
Let's look at the last option, change parry and riposte. An opponent beats for several reasons: (1) to annoy you, (2) to provoke a response either for reconnaissance or to create an opening, or (3) to remove the blade from the line to facilitate the attack. For this discussion, we are going to refrain from responding to either case (1) or (2), and instead focus on (3) the beat to remove the blade to clear the way for the real attack.
When the opponent beats your blade, there is an energy transfer from the attacking blade to yours. This is what propels your blade out of the line. But at the same time, the beat overcomes the inertia inherent in your blade in a stable guard position. The beat gets your blade moving. The question is now who will profit most from that movement?
A beaten blade often does not go horizontally from 4 to 6 or 6 to 4 or 3 to 4 or ... Instead it has a tendency to pivot around the anchor point formed by your hand and wrist, moving through part of a circle. The amount of that movement depends on the strength of the beat, the inertia of the stable blade, and any effort you put into resisting the beat. We can use that direction. As the blade starts to move use the fingers, hand, and wrist to take the blade through the teardrop shape of the change parry ending up with the opponent's attack displaced by your parry away from the target (whether the core in foil or also the head and advanced target in epee and sabre). Because the opponent will be lunging or fleching or flunging at this point, a quick retreating step aimed at controlling distance would seem to be prudent, with both feet down at the instant of the parry to allow an immediate lunge in the riposte if needed.
Sabre presents a special case. Lateral parry responses to the back edge beat have a nasty tendency to carry the beating blade immediately into target - you can hit yourself with your own parry if you have not managed distance effectively. The 7th parry is one answer, but requires an inordinate amount of practice to develop proficiency and is pretty much useless for anything else. That leaves the change parry as a viable response to a back edge beat.