Encourage them to be honest with you by doing the same, or, better yet, by doing the exact opposite. Deceit is your friend here. Your parents are learning every day and will be suspicious if you're nowhere to be found on the Internet, but if you give them the impression that you spend time on a well known site that parents have easy access to, they'll tend to flock there themselves. Parents love Facebook because of its bright colors, and you may find it helpful to keep a Gammy-friendly account there so you can keep an eye on them.
"Status updates about her doing homework and opening a savings account? This all looks legit."