Indeed. I probably would not have thought to look there, especially when I've never done anything involved with the Share system, so I wouldn't have stumbled on it. My instinct would be to look at notification settings.To be fair, it's pretty natural to assume that if it could be turned off, it would be settings>notifications... but that's not where it is. I had no idea until this thread that there was a separate menu for share notifications.
It didn't particularly bother me in Arkham Knight, but I'll happily disable that. Good to know.