To answer your question directly - yes, there's a rule to put in .htaccess for this. It would be something like:
RewriteRule (.*).asp$ http://www.link.to/ourbrandspage (someone who knows regex better may correct me on this)
However, redirecting everything to the same page is a bit of a waste - if the site has been around for a long time, then there may be inbound links to deep pages in the site which would be better off being redirected to the appropriate page on the new URL structure rather than dumping everyone on the same page.
If there's a pattern match which you can follow, then you can write regex to cope with this (e.g. if the old structure was http://www.whatever.com/blah.asp and the new one is http://www.whatever.com/blah.php then just do an .htaccess redirect from *.asp to .php - something like RewriteRule (.).asp $1.php). However, I'm going to bet it's not that simple.
Best is to do a proper map of existing links so you can direct the actual old URL to the most relevant URL on the new site.
I've had to do this kind of "emergency redirect fix" before, for sites with a lot of pages and no neat "pattern match" fix. The way I usually approach it is to try and get a list of the existing URL structure (either: from a back up version of the site, from Google analytics, from webmaster tools or at a pinch you can scrape the SERPs) to grab all the possible/indexed URLs and stick them in a spreadsheet. I then prioritise the highest traffic pages - if you can see via Google Analytics (or server logs) which pages get the most inbound traffic, redirect those first to the most appropriate page on the new structure. That way you can carry on adding new rules into the .htaccess as you go along - you'll probably find of the 1000s of old pages, there's a relatively small %age which get the vast majority of inbound traffic.
Hope this helps!