Can Sprint tell if your iphone 4 was jailbroken?

So I jailbroke my iphone 4 and something went wrong the camera roll wasn't saving pictures so I deleted Cydia and restored my phone but the camera roll isn't saving pics. I restored it like 3 or 2 times. I'm wondering can they find out and also is there a way to fix it at home probably?

I don't know of any way you can fix it at home but I can tell you anyone who knows about phones and devices, especially those who spend their life working with phones, will easily know if the iPhone has been jailbroken.