Hello Ryan,
Off of the top of my head I don't believe that there is a way to do that unless you created a user to always be logged into that phone. If you did that, you could set up a Recording Policy to delete any recording generated by that user. I did find find this Idea that is currently marked as Future Consideration in the Product Ideas Lab. I would recommend voting and commenting on that Idea to let our Dev team know that this would be a useful feature.
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Jason Kleitz
Online Community Manager/Moderator
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