To remove a contact, tap on the green Family button on the bottom toolbar. Now tap on the "Edit" button on the top right of the screen.
A red trash can will appear to the left of every contact, tap on the trash can next to the contact you would like to remove.
When you're done, tap on the "Done" button on the top right of the screen.
You can also click cancel to exit this window if you do not wish to delete a contact or pressed edit by by mistake.