No, it is not possible to not accept a badge.
As far as I am aware, there is no functionality that would prevent you from getting the badge.* As I mentioned in the comments, maybe just move on. It is not such a big deal, really. Although badges are nice and give you a sense of achievement, it is hardly the case other users really care about what badges you have in your virtual pocket.
*: an individual user can ask the community moderators to dissociate a post from their account. It is not clear to me if this situation is a proper use of this functionality, so we can wait for a community moderator to chime in.