Thought I should post this here, maybe it’s even worth a tip article on thurrott.com
“Thank you for all of the great feedback, and for using outlook.com! I just wanted to let you know that everyone should be able to clear their search history now.
To do this follow these steps
1) Click the Gear/Cog in the top right hand corner
2) Click Full Settings at the bottom of the Quick Setting Pane
3) Select General in the left
4) Select Export
From here you can delete your search history, export it if you want a copy, or request an export of your mailbox.
Hope this helps!”