How can I delete offensive emojis on my iPhone keyboard
Unfortunately, there is no way to edit the Apple Emoji keyboard.  You can, however, turn it off, by following the instructions posted at the following question:
How can I remove Emoji keyboard from iOS8?

Settings → General → Keyboard → Keyboards. You'll see English and Emoji.
On the top right corner is the word Edit. Press Edit, and then tap the red button followed by Delete to remove the Emoji keyboard.

Additionally, you may be able to find a 3rd-party Emoji keyboard on the app store that is customizable.