I've done this in code in vb.net/c#.net, where you pull messages from an SMTP server, and then you can do what you want with them: delete them off the mail server, save the messages, save the attachments, etc.
I would reckon in SSIS you'll have to put the same code in place; i don't remember seeing a component to read email directly.
you could also create some CLR methods to do the same work as well, since it's the same code.
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