Child profiles can be deleted within your account settings. You'll need to do this on the website.
1. Go to your BBC account settings
2. Click into the Children's settings tab from the menu on the left-hand side
3. Click on Delete child profiles
4. Select the child profile you want to delete
5. Click the Delete button to confirm
When using the iPlayer TV app after removing a child profile, the profile may still show. Selecting the profile will refresh the account and it will be be removed.