I have a TT-01 with ABS tires and it does the same thing. If you just let the TT-01 spin out constantly in a circle you will notice the clockwise circle is bigger than the counter clockwise circle. Try the same with the car going in reverse and you will get the opposite result. It seems to me that the TT-01 is not a balanced car and the weight of the battery and the torque from the shaft drive is causing this.

I am going to try:
Light weight lipo battery back &
Install anti-sway bars for TT-01

Both are relatively pricey options for the TT-01, so I might just try a TA-05 instead, or you can always practice more (free and more fun =])