Don't eat the cookies.
I'm about 90% certain what you are talking about is not stored in a cookie from bj21. I think it is an index file that is stored in the temporary internet folder and is part of the browser history. You can 'clear history' and reset everything. Or you can reset your history archieve's to the minimum of 1 day. That way you start with a clean slate everyday.
But just to be sure, do a file search for bj21 and see where the cookies and files are being placed on your computer. Then delete from there.
BTW, If you don't want to accept cookies from bj21, or any other site, then just add them to the restricted site list in your browser's security settings.
RB