We don't know how the SMG works. Does there exist send connector on your Exchange server to send emails to that application? If so, try to remove that send connector. You need to prevent outgoing email through the left part, make all you outgoing email through Edge server rather than "Exchange on-premises → SMG →PGP → Internet"
There only can exist Edge server between Exchange on-premises and Exchange online. So, if email through the left part, it will cannot send to Exchange online. You can try to add your application before the EOP, if they are supported.
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