If you mean "Recent Stuff", then I'm afraid there's no such option by default, and I don't see a way of how to implement it... if you take more closer look, you would see this page at the bottom expands to a navigation of older pages, which list all topics in the order of new topics or recent replies appearance. So if you remove some topics from the first page, what to do then with the other older topics? May be completely remove this navigation and don't offer it, but it is truly very useful on many forums...
Also, even if we would suppose that we could remove some expired topics, then you may have a situation, when the initial first page would be completely empty, 'cause all topics expired and removed.
The most easiest way to keep the first page without this stuff, is to switch to the "classic" forums mode (setup_options.php -> $startPageModern=FALSE;).
I suppose you may also try to edit bb_func_ldisc.php and rewrite basically all requests, which generate the standard output, adding a condition to mySQL to compare either topic_time by some period, either topic_last_post_id to the necessary post_id.
So answering your question - there is no such option, but it's possible to code it, putting some extra efforts (as always).