The access is granted using your Twitter account. See below for revoking access from Twitter.
More info can be found in their FAQ:
I’d like to opt out and not have my tweets shown on Favstar or on Favit. If your account is active and unprotected on Twitter, then write @FavstarHelp a tweet asking to opt out. This shows that its your account and prevents others from opting you out without your consent.
If your account is protected, or has been deactivated, please send us an email to [email protected] including your username and a link to your page on Favstar, and well organize to have you removed. Please do not send us a tweet if your account is protected, as we will not be able to see it.