I found the answer to this question. outlook.com, aol.com, and probably other sites use Facebook's "search for a user by e-mail address" feature to find your profile and use the profile picture.
To prevent your picture from appearing, you must go into your privacy settings and change them so that people cannot find you by entering your e-mail address.
I found the answer here, under the question "What information is shared between Outlook and Facebook or Twitter?"
Outlook privacy - Outlook.com
To change your Facebook privacy settings, click the settings icon at the top right of your Facebook page and select Privacy settings. Then under "Who can look me up?" change who can look you up using your e-mail address to either "Friends" or "Friends of friends."