The expression used for giving rein to a horse as he extends his neck out over a fence as he jumps it is the "release." You are supposed to "follow" with your "release" in order to maintain the correct contact with the horse's mouth. Not properly following a horse's extension over a fence will get you screamed at faster that almost anything because it can seriously interfere with the horse's effort and quickly lead to a horse who is either dangerous over fences or won't jump at all. Every student has had an instructor scream at them, "GIVE!" if they are the slightest bit sticky in reaching forward to allow the horse full extension of his neck.
This poor rider seems to be a bit of an overachiever when corrected by her instructor.
Actually, it looks as if the reins broke, but I couldn't resist my little story.
All joking aside, one should NEVER EVER be pulling backward on the reins over a fence. The rider should be completely balanced and independent, so that they can throw the reins away entirely, if need be, and remain perfectly over the horse's center.