How does Twitterfeed deal with past-dated items?

This depends on the feed settings in twitterfeed. If you select "by pubDate", then it will read the piblish date of the item in the feed, and only post ones which are newer than the newest previously posted item. So if there's a new item with an older date, it will not be posted.

If you select "by GUID", then it will ignore publish dates and look at the items' GUIDs instead (this assumes that your feed items contain GUIDs of course). An additional option in this case ("feed is sorted") determines whether twitterfeed only checks at the top of the feed for new items (i.e. new items always get added to the top of the feed), or whether it will scan the entire feed to find new items (if new items may be added in the middle of the feed). In that last scenario, there's a danger that it will eventually post all items in the feed, however old, so use that with caution.