Sorry about that. Until the proper fix is in place you can clear the notifications manually by going to your Notifications tab – http://discourse.example.com/users/username/notifications – and then click on “Mark all as Read” button.
I looked into this bug today and it seems like this issue has been present in our source code for a while. There is no code handling this case (i.e. marking invite accepted notification as read) at present.
In my opinion “Invite Accepted” notifications should show up as read, like we do with badges notifications. This will be useful in case of “Bulk/Disposable Invites”.