The only way to remove friends from the game is by removing them from your Facebook account. This means you have to unfriend them, if you want them to disappear from your friend list in the game.
You just unfriended someone on Facebook and you wonder why they still show up on your friend list? Well, it can take up to 24 hours until the list refreshes. You can interact with the friend as long as they are on your list, even if you already unfriended them on Facebook.
Keep in mind there is a limit of 151 friends at the moment. If you have more friends than 151 they won’t show up. Sometimes it makes sense to remove some friends from the game.