One option worth checking is whether you're using trunk-side recording. If so, under External Trunk > Recording, there's an External bridged transfers setting that controls whether recording continues after an external-to-external bridged transfer.

In the screenshot below, the External bridged transfers option is disabled. With this setting disabled, recording should stop once the call becomes an external-to-external bridged call, provided the call remains under trunk-side recording.
Another approach, if it fits your telephony architecture, is to use Release Link Transfer (RLT). When RLT is successfully completed, Genesys Cloud sends a SIP REFER to the carrier and removes itself from the media path. At that point, the carrier handles the call directly between the external parties, so Genesys Cloud is no longer able to continue recording the conversation.
I would also confirm whether you're using station-side or trunk-side recording, since the External bridged transfers setting applies only to trunk-side recording. With station-side recording, the recording continues after an external transfer and this behavior isn't configurable.
Has anyone else implemented this approach in production? I'd be interested to hear if it resolved the issue or if there were any carrier/BYOC-specific considerations.
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Raphael Poliesi
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