Can outgoing text message notifications be disabled from appearing in car's Bluetooth system?

[Curlysoni]

I just recently got a new Moto X4 (previously had an HTC One M7) and use T-Mobile as my carrier. I have paired up my new phone with my car ('16 Honda H-RV) via Bluetooth with no problems. The only annoying issue with the new phone is my car keeps notifying me that I have a new text message when I'm sending out a text. Example: I'm sitting in my car waiting for my daughter to get out of practice and I send her a text to let her know I'm outside waiting for her and when I do my car will notify me that I'm receiving a new text. Very annoying!! My HTC never use to do that. Is there any way to disable the notification for outgoing texts so they don't appear as a new text message in my car??? Any suggestions are much appreciated!