I have been wondering why they need access to the GPS, and why they need to contact their own site after the speed test has completed. It seemed like they were building up some kind of database of speed test results at different locations, but I don't remember ever being told about this when I installed the app.
The answer seems to be in their blog at
Xtreme Labs Inc. — Web & Mobile Redefined. . They have a map of the world showing average upload and download speeds for each country. They also say that they might do more in the future with the data that they have collected.