watch shows text message notification for group in which notifications are turned off on phone

Garmin displays those notifications that the app sends to the notification API. If notifications from contacts that you blocked within the app, are being sent to the API, it is a problem of the concerned app, not of Garmin. Garmin is not supposed to do any filtering, it is the role of the app.

The app settings are custom for each app so they can't be queried. What you need to do is to make those notifications not being sent at all. So, tell your car to stop spamming :-)

so I can't tell my messaging app not to do a notification on the phone, and that works, but it will result in a notification on the watch regardless?  
unfortunately can't turn off the car ones, but I'm surprised that there is no way to control which messages give notifications on the watch since you can control it for the phone.

How do you control the notifications on the phone? Is it in the app settings or in the notification settings for the app (the one you see when you go to App Info for the app)?

thanks for replying!
it's in the settings for the messaging app, you can control notification type for each conversation (sound, silent, none, etc). in the general settings you can control whether that app can notify, but not at the per-conversation level.

That is the issue here. One is the custom app settings and one is the system settings for the app. Custom app settings is...custom...and nothing Garmin knows anything about.

Ask the developers of that app if they can fix that in some way. The notifications are generated by the app so they can be stopped from being generated.

"Ask the developers of that app"
it's the messages by Google app :)