I agree about the synthroid - I think I would sit with them and explain the importance of GH and what you feel are the reasons for it and try to explain why it is important. I have heard parents say 'if it is just so she won't be a little shorter why would I do it?'. You need to reiterate the importance of treating the thyroid and why this is life sustaining and if they quit following up with you or don't fill it then I would report it.
It may just be that they don't understand the importance of treatment. Document the discussions and try to protect your patient - the child.