You're absolutely free to deny that permission. It's not stated explicitly, but the contacts are never transmitted to our servers. The only reason we ask for them is so that if you view your Ting bill, you see friendly contact names rather than a phone number you might not otherwise recognize.
The app works fine without the permission.
If you're still not comfortable with the app, the mobile website should suffice for most things. Just access ting.com on your mobile browser. Everything should be there, including billing history, device settings, usage info and your RAF code.