Before 8.3, I was able to clear recently used emoji by clicking on Settings->Reset->Reset Keyboard Dictionary. Now, that does not work.
My recent emoji screen is littered with accidentally typed ones and such. It seems though that you can place your favorites on the first column by re-selecting them from their original lists (screens), but that does not seem to work well, and it is not as useful as being able to clear the entire list of recently used emojis.
Best Answer
So I figured out in iOS 8.3 when you reset your keyboard it doesn't clear your recently used emojis. But it replaces them with random emojis.
Then try typing an emoji. Now it should be first in your recently used. So just pretend the default emojis aren't there.