You do NOT have to register the Garmin Traffic Receiver. In fact you CAN'T!
I received mine and attempted to register it as the instructions with it indicated. I went to the Garmin website it mentioned and I could not see where the registration would be possible. I called Garmin and waited on hold for almost an hour. When the agent came on I asked the exact question you just asked. She kind of laughed and said, "I don't know why the instructions with it say to register it, because you no longer need to. Just start using it in your car and it'll be fine." It does seem to work fine.
So hopefully I just saved you an hour of wasted time. You're welcome. :)