The ex-girlfriend is under 18 and the OP is wondering if her parents can go online and see if the OP and the girlfriend are texting each other.
Short answer: Yes they can see that you are communicating with each other especially if her parents are paying for her phone and service. They can't see the contents of the messages though through the website. However, because the parents are paying for the phone, they have every right to see that phone and compare the usage with what is stored on the phone. If it doesn't match, then the parents have the right to remove the phone from the girlfriend until a time the parents set.
Okay maybe that was a long answer.
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