If I wild card the BoP ata

Once per turn a friendly character using this team ability may use support as a free action. When it does, it may only target a friendly character with whom it shares a keyword and it subtracts 3 from the d6 instead of 2.

What exactly can the trip Girl bystander tokens do?

Nothing...

The bystander tokens of Triplicate Girl have no keywords attached to them, so this ATA will not work.

The part of granting the character (Trip girl) support and the clause for the stipulations are two different sentences. If you gain all the text on the bystanders do you get to fully utilize the black light ring on her.

Edit: Are you asking if you can copy the team ability with the 3D Triplicate Girl, and now that she can use Support, the bystanders get Support through her trait without the restrictions (though not as a free action either)? If so, the answer is... uh... I'm not sure.

That's exactly how I'd interpret the interaction, at least until someone actually using the BoP TA uses Support that way.

Yeah, I'd think that would be the end result. Support is a power. 3D Triplicate Girl can use it. Therefore the BSTs can use it. "Once per turn a friendly character using this team ability may use support as a free action. When it does, it may only target a friendly character with whom it shares a keyword and it subtracts 3 from the d6 instead of 2." is not a power (it's an ability), nor are any of its parts except for Support. The BSTs can't use any other part of that, so it doesn't apply to them.

(I'd post Triplicate Girl's trait for reference, but I have to get to a game!)

So the Bystanders can "use" support, but can't target anyone with it because they don't share keywords with them.

Unless the both the BoP figure you're trying to heal and the Triplicate Girl bystander token have both picked up a Legion ring, or if there were two on the field, a Nova Helmet.