Looks like a riding form of an overcheck or bearing rein to be. I'd be careful. Just because it attached to the horse's pollstrap doesn't mean it isn't pulling on the bit- because the bridle is attached to the bit. All its really going to do is pull up so that its not your hands that are doing it. It won't change anything as far as hardening or yanking on her mouth.
What about pulling up, push her into a tight turn, and sending her forward? That way you aren't allowing her to go forward as a reward, but rather making her move her feet but not go anywhere. Other than that I'd use the dressage whip method and give her a good swat under the neck. She's not likely to try it again.