The contacts that you see in WhatsApp come from your address book. There is no way to directly edit the Contacts screen.
To delete a contact from WhatsApp Favs screen permanently, you will need to delete the contact from your phone's address book.
In order to remove a WhatsApp contact from your phone's address book:
Then, refresh your WhatsApp contact list by opening WhatsApp > Go to Favs screen > More > Refresh Favorites.
To delete a contact from the WhatsApp Favorites screen temporarily, you will need to delete the contact from the WhatsApp Favorites screen without deleting the contact from your address book (will remain in the Contacts screen). To do that simply:
If you still see the contact after it was deleted, it is likely that you are seeing the conversation on your Chats screen. To delete a chat, simply tap and hold on the contact and then select Delete chat.
To add the contact back to Favorites screen, you will need to add the contact back to your phone's address book.
If the contact is still in the address book, but doesn't appear in the Favorites screen:
Open WhatsApp > Contacts > Long press the contact > Tap Add to Favorites.