As a thought, try turning off your cookie support in your browser as a test. That might change the behavior and get a different reaction from the scanner.
The site is running on PHP, the cool part about that is that most of the calculations are being done on the server. Again, Linux as a server is less likely to be aiding the 'dark side' in sending you that kind of trojan. However, anything is possible these days.
My . 02 is that the 'signature' which the scanner is looking for is being duplicated by an unfortunate string of code in the TDR's webpage. That code is likely harmless but is fooling the scanner into warning you.
You are doing the right thing looking into it, press on until you figure it out. Someone else is bound to see the same thing if it truly is coming from the TDR.
If I had the same software suite I'd test it for you.