Are you getting just the single Alexa "item" from Ad-Aware? If so, that one unfortunately goes more or less hand-in-hand with IE (IE-6, anyway) and you're probably stuck with it -- it's tied into the "related sites" function, among other things.
There seems to be a general consensus that if you stick with IE, your best bet is to simply add it to Ad-Aware's ignore list. I also had to do that with my "about:blank" home page, Ad-Aware doesn't like that either because of the worm that uses it as a starting point or hook.