We've created a group for "Founding Members" so we can give them a special badge...

But the "rank" badge is showing up as well.

Since we've just switched to invision, our founding members (who have lots of posts in the old platform) are getting a badge for our newer members --- which is kind of contradictory.

Would be great to exclude the founding member group from the "ranking" system so they don't get these rank badges

The defaults are rather limited and very newbish. You can edit/remove them here:

https://mysite.com/admin/?app=core&module=membersettings&controller=ranks

Alternatively you can remove it from the theme for those groups.