Yeah, that could be annoying for sure.  Most accidents don't result in a totalled car or branded title, so if you're trying to filter out any car that's had an accident, that's not currently possible.  Unfortunately we don't currently have access to that information from most sources.  (The carfax information that appears on the Cars.com detail pages isn't included in the feed they send us.)  I'll certainly keep this request open though; maybe we can get that added in the future.

In the meantime, if there are common phrases you're noticing in the vehicle descriptions that note there has been accident damage, you could filter those out with negative keywords or key phrases, using a minus sign followed by the word or phrase, like -"accident damage".  But as I said, the specific section you mentioned that's provided by Carfax doesn't appear to be part of the vehicle description that we search on, but a separate section entirely, so this would only work for accidents mentioned in the description itself.