Somewhere in the setup section of your typoscript page template, you just have to add the following line:

plugin.tt_news.getRelatedCObject.10.default.20.strftime = %B %d, %Y

That will display the date in a typical American format.

Now, I haven't yet checked, but I think that only changes the date format for related items that are regular news items and not for links to pages. If that's the case, you should probably find that modifying the date format for other types of related items would be similar.