Righto, I'm not going to pass judgement on the person who set up the calendar except to say "Don't let them do it again".
From the looks of that icon and the fact that you can't find it under Recipient Config --> Mailbox, I'd say it's a Public Folder with a calendar bolted on. Hence why you can't see it in the aforementioned location.
Go to Toolbox --> Public Folder Management Console. Have a look there for it.
Recommended reading: http://technet.microsoft.com/en-us/library/aa998834(v=exchg.141).aspx
Give that link a go and if that doesn't help, we'll move on to plan B.
nyah nyah nyaaaah
