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For the most part it involves trust; unless you are willing to do some digging. DNT+ is not open source, but you could ask the company for the source code. If they oblige, you could see if there were any quirks.

A second and more accurate option would be to setup a packet sniffer and see what kind of traffic the software is sending home.

To be honest, the question from your boss applies to any software. You could ask the same question of any software he or she has installed.