Don't worry, members will not be notified when they are removed from your friends list!
Web
Hover over 'Social' on the left menu and click 'Friends.'
Find the friend you want to remove and click the icon on the right side of their image.
Click 'Yes' in the text box that appears - This will remove the member from your friends list!
Mobile
Tap 'More' in the bottom toolbar and select 'Friends.'
Tap the icon to the right of the friend you wish to remove and choose 'Remove Friend:'
Alternatively, you can remove a friend from within a game by tapping on their avatar and selecting 'Remove Friend:'