I've got a query re the use of attachments

Player A has a character with Taste for Blood attached

Player B takes control of that character

The attachments stays attached (it is still legally attached) but it is still controlled by the owner

Attached character gets +1 STR. Response: After you lose a challenge as the defender, attached character claims 1 power.

Can the reponse still be triggered, presumably by player A (The controller of the attachment)

I aslo assume this still refers to when player A loses a challenge as the defender

Yup. The +1 str is constant, so it'll stay in effect. The response can still only be triggered by the controller of the attachment, and refers to when the controller (of the attachment) loses a challenge as the defender. Mind you, it'll give the character that power, so there's not much incentive to trigger it unless you have a way of stealing that character or the power back.

Ellaria Sand comes to mind for the latter.