How do I remove the latest activity update in the profile header?

If you're trying to remove the latest activity text from your profile header and it doesn't exist in the activity stream you can manually delete it. In your child theme's functions.php file add the following:

delete_user_meta( $user_id, 'bp_latest_update' );

Where $user_id is the ID of the user you want to delete the text for. In most cases the admin account has a user ID of 1 e.g.

delete_user_meta( 1, 'bp_latest_update' );

Remove the code from functions.php when this has been successfully removed.