If you open the .tdf file of the track you will see that the driveable materials (ie. grass, road, gravel, etc.) each have their own skid texture that gets applied.
In the example below the material called "road" uses a texture called skidhard.tga for skid marks.
In your case it might be better to use a completely clear texture.
// Roads
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Dry=0.96 Wet=RoadWetGrip Resistance=1700.0 BumpAmp=RoadBumpAmp BumpWavelen=RoadBumpLen Legal=true Spring=0.0 Damper=0.0 CollFrict=0.4 Sparks=1 Scraping=1 Sound=dry
Reaction=tiresmoke Tex=smokewhite.tga Max=1024 Scale=(1.0,1.0,1.0) Growth=(4.0,3.0,2.0) ASDEnvelope=(2.0,0.2,3.5) DestBlend=InvSrcAlpha SrcBlend=SrcAlpha
Reaction=skid Tex=skidhard.tga Max=2500 Pixel=NoReduceDetail Particle=Plane+Deformable+SingleSided DestBlend=InvSrcAlpha SrcBlend=SrcAlpha
Materials=road