Using the refresh on-demand option is fairly straight-forward.
To request a refresh of a website thumbnail, you simply add &redo=1
to your request. That will re-queue that thumbnail for re-capture in the regular queue.
Warning: Be sure to put this tag somewhere in your request BEFORE the &Url. Otherwise, the tag will be ignored and becomes part of the specific Url requested.
This feature is useful for those what want a "before" and "after" history or who queue a lot of broken requests (typically foreign domains that are down at the time of request) that are working now.