The GUI password, or the router access password, as in the one needed for a computer to be able to access your wireless internet? What brand is your router?
As for the router itself, yes, it's the consumer's responsibility, but changing a password shouldn't be very hard.
If I remember correctly, you only use an IPhone, right? Nothing else? If only an IPhone, that could pose a problem with changing the password for wireless access, but I'm not sure. It's possible that you may need a direct connection to enter the GUI so you can change the wireless access password. Again, I'm not sure, at this point, anyway.