If you click the X on a cross-wiki notification, it disappears from the UI, but it's not marked as read on the remote wiki. If you refresh the page, it comes back as unread. AFAICT no XHR request is sent when I click the X.
Additionally, clicking the X for the group item containing foreign notifications also doesn't do anything (apart from hiding the whole group item until you refresh the page).
Update 2016-05-14 01:15 UTC: it looks like this may be caused by PrivacyBadger. To work around that, we'd have to proxy mark-as-read requests through the local API.