Multisite: Deleted sites show as "phantom" sites on Jetpack -> Sites

I recently deleted several subsites in my multisite installation. They are marked as "Deleted" if I go to http://domain.tld/wp-admin/network/site-info.php?id=XX :

But on http://domain.tld/wp-admin/network/admin.php?page=jetpack I get this:

Now, this might very well be limited to my own multisite. I recently switched host, and cleaned up a lot of cruft while I was at it, manually deleting tables and such for many subsites. So, ideally someone would test with another multisite network to see if they can reproduce this.

Reproduce this on a WordPress multisite by deleting subsites, then inspect the Jetpack network admin page at wp-admin/network/admin.php?page=jetpack and compare it with network site-info.php entries marked Deleted. Done means deleted subsites no longer appear as active or phantom sites; the issue names no source file or test, so further code entry points must be located during investigation.

Written by the indexing model from the issue text.