Thanks for your post.
Attachments are not currently a part of the data structure that returns the Outlook context the user has selected. That's why you cannot access them, unlike email addresses, subject, body etc.
It seems like that would be useful, and I would suggest making a post on the Salesforce IdeaExchange to that affect to get the teams aware of it. (https://success.salesforce.com/ideaSearch)
If you're ok being reliant on the end user saving the attachments, you could gain access to the SFDC content documents that are saved by searching for the subject in the tasks, and then use that record to find the related ContentDocuments that are available.
(Tech. Writer at Salesforce)