Gaige's regain was under Duty, but the thing here is, that's actually a bit weird for her! In general, she doesn't have a heavy sense of duty, and is a lot more about pursuing amusement or satisfaction. That being said, she won't actually change all that much with this part of her missing. She might be a little less apt to try and herd people in her group around, but she'll still want things fixed for the sake of others, so she won't be totally useless.

Her regain totally involved blatant murder, though, so that might be fun.