Stop recording for Attended Transferred calls

Howdy all,
in a call centre environment the Operator takes the call → the caller ask the agent to speak to contact → the Agent calls the contact, announce the caller, connect the Caller to the contact.
At this point I need the Call Recording to stop as the conversation between the Caller and the contact is Private.
I cant seem to find any ways of doing this.
Any help is greatly appreciated

Happy thanks Giving!