Closing or "deleting" your account is as simple as logging out of Twitter Counter and removing permission for our app The Visitor Widget from Twitter's settings page http://twitter.com/settings/connections.
The data we collect is publicly available via the Twitter API. All visitors to our website can track the basic statistics for every Twitter user available via the Twitter API just by typing their names in the URL. We use the collected data to create a page with a historic graph of a given user's Twitter statistics. Tracking and displaying this data does not constitute an account, but merely a page on our website.
Only when you have signed in to Twitter Counter via our login button and have gone through the OAuth process do we create a personal account associated with your Twitter user. This account, as stated at the top, is quickly closed or "deleted" by logging out and removing permissions.
I should add, as a side note, that the numbers we collect are always available and visible on your own Twitter page, even if your account is set to private.