Rechecking is an important part of fixing links. If your site is a large one you won't be wanting to run an entire scan of your site, just recheck the parts you've fixed.
Rechecking in Integrity has traditionally been limited to re-testing link url(s) that Integrity holds. This is fine if you have fixed the link by correcting the target. But if you've fixed the link by editing the target url of the link, or removed it from the page altogether, then it's necessary to re-check the page that the link appeared on.
New in version 9 are options to re-check a link url(s) or to recheck the page(s) that a link appears on. It's possible to select multiple links / pages before choosing these options.
These are best accessed via context menus in the links views. Be aware of whether you're selecting link urls or the 'appears on' page url. The options you see will be tailored to what you've got selected.