Traffic Travis uses several sources of backlinks data; that's why the values displayed in the Dashboard are different from the backlinks listed in the SEO > Backlinks tab.
The total backlinks count on the Dashboard is provided by MajesticSEO but the list of backlinks (URLs that you see when you use the SEO > backlinks tool) is given by up to five different sources: the top 1000 from MajesticSEO, Moz, and Alexa, plus Blekko and Exalead.
If your backlinks have not been indexed on any of the sources mentioned above, TTv4 will be unable to detect them in the reports. It will instead show a message saying no data is found for the URL.
To make sure Traffic Travis finds as many backlinks as possible for your site, go to the Link Analysis tab, then click on "Advanced Settings." Check all 5 backlink sources (see below).
Be sure to click OK to save any changes.