The Alert Bar is controlled by a Link List. You can edit it by going to Content > Link Lists > Alert Bar. 

The Name of the link list is call to action, the link is where the call to action takes the user, and the description is the text that shows before the link. You can set the icon you want using the "icon class" field. 

A full list of icons available for your theme are listed here: http://mk037.monkpreview.com/_assets/fonts/icons/