First, you should be mroe specific about "distortion" and describe the best you can what you hear.
Second, I do not think you need that adapter for what you are trying to do. It is designed to take high signal levels from an already amplified signal and covert down to low level signal for an amp. In this case your soundcard is already at a low/line/preamp level. I'm not 100% positive on this specific vehicle but logically you should be able to connect the soundcard directly to the factory amp if you hacked up some 3.5mm cables and wired it directly in.