My question would be ...does she have a functioning thyroid? If its been removed/born without one/ killed with radiation then serious action is required. If not then let her feel like **** for a while. She will learn quickly enough.
Is the cost of the med an issue for her?
Depending on what her condition is to start with, she may herself notice her symptoms worsen. For example if she is hyperthyroid to start with and not take the medication, she can expect to feel anxiety, jittery, lose weight, have heart palpitations, and insomnia. If she is hypothyroid, she may gain weight, feel sluggish, and tired alot, and feel depression. These are the most common effects of those diseases. It can take months or weeks for the symptoms to develop, depending on how bad she was to start with and her dosage. Be vigilant and keep an eye on her.
You can talk to her till the cows come home and I bet she still won't take it. Sadly you will have to step back and let her find out for herself how it feels not to be on the medication. You could ask her doctor to call her and talk to her, it may or may not help.
You could print out information from the net to show her, too, but I have seen this sort of thing from young adults and they do need to find out for themselves the consequences.
Good luck.