The bit I assume you're referring to is the text that pops up halfway through:
The threads below have not been updated since your last visit but still contain unread posts.
Bear in mind that the favourite forums list is not supposed to be a list of new posts - it is a list of unread posts.
Things above that line are new posts that were made after you last visited the forum. Posts below are the unread posts that were already here last time you visited the forum, but you did not read.
If you want to clear out the list, you need to hit 'Mark Forums Read' in the 'Quick Links' dropdown near the top of the page. That will mean all the threads you saw but did not choose to read in that visit will not turn up next time.