QuoteURL is a way to keep tweets grouped together that might not be in a threaded conversation.  Also it grabs them before they might get washed away but the tide of tweets over time. To grab a tweet you must get the individual status URL from the web itself and paste it into the site.  If you wish not to log in, you can grab up to 4 tweets.  If you decide to log in you can get up to 10.  This helps control the API limits that might be encountered...