On the Varrock Task page, it fails to mention that after completing the Hard tasks, you can speak to Vannaka to change the point of your Varrock Teleport spell/teletab to the Grand Exchange.

 

I forgot to take a screenshot I'm sorry, but it is easily verified if you just go talk to him and ask about the Task system. The following chat box will have the option for changing teleport location.

It actually unlocks as early as the Easy tasks, which is listed in the guide. You can talk to either Rat Burgess, Vannaka, or Reldo. I know I talked to Reldo, personally, when the update first came out.

 

I don't know though if, say, you completed the hard task lisk you could change your spell with anyone but the guy in charge of hard tasks (Vannaka).

Ah ok, I missed that. I only saw it after I completed all the Hard tasks when speaking to Vannaka, so I figured it was a new one. Thanks.