It's not clear if the badge ended up on the profile of the person you accidentally bestowed it upon. If there's anything to remove, a Team Member could remove the badge from the person you didn't intend to give a badge to. (Because that person isn't a member and has a private profile, only a Team Member can do anything with the profile.) Then after the 24 hours has expired, you could give the badge to the intended recipient.
And, meanwhile, thanks for your effort to thank Billie Keaffaber!