That's expected. Removing that permission "Controls the preservation of RECEIVED headers in messages. If this permission isn't granted, all received headers are removed from messages." When you send the message externally, that last hop is not your org receiving it, its the recipient's org.
https://learn.microsoft.com/en-us/exchange/mail-flow/connectors/send-connectors?view=exchserver-2019
The header stamp showing the receiving connection between the Exchange Server and a receiving external server is not something you can control.
You can also clear the FQDN on the send connector, but I wouldnt do that. It should match a subject name on a certificate bound to SMTP and you could get mail rejected that you sending.