Uh, point of order - Steph's NOT running around in her costume. That's Cass's outfit. (Or Huntress's, if you want to be pedantic, but she hasn't laid any claim to it since Cass took it over, so we'll consider it Cass's for all intents and purposes.) As such, she had every right to hand it over to Steph, and Steph has every right to wear it - it was a gift, after all. Babs would be within her rights to say that Steph couldn't call herself Batgirl without permission, given that she created that particular alias, but she (Steph) has a perfect right to wear the costume if she wants to.