Per these words from the T-Mobile Tuesdays page:
Participants who enter a valid and eligible T-Mobile phone number will be sent an SMS text with a confirmation code.
Since you get the code via SMS to the number provided, if you have used it before, you couldn't register again since then, if you did so, you would get double rewards.
There is this page which you can visit without a code.
Hey there What specific plan do you have on your tablet? Is this a pay as you go account?
Yes. It is a pay as you go account. I assume that means that I am not eligible for T-Mobile Rewards.