could the white rope be part of the container and not the parachute itself that was dyed pink? see photo of the clips being tied back..
It is unlikely that the white rope came from the pink reserve. Also, there is nothing conclusive to prove that the white rope came from the missing reserve. Who knows, the missing reserve may have been dyed pink as well.
Reserve chest parachutes were in very short supply in the 1960s. The one in question was probably dyed pink to identify it as belonging to the skydiving center where it came from. What was in the missing reserve was apparently junk from damaged reserves or other sources. So who knows if it was white, pink, polka dot, or some combination of these and other colors.
Based on the appearance of having been heavily used, it appears to me that the source of the white rope remains to be seen. Again, based on his inspection of the pink reserve, maybe Tom Kaye could comment further.
And if the white rope came from the missing reserve, why didn't Cooper just leave the remainder of the canopy on the airliner as he did with the pink reserve? If he threw that canopy out the back of the aircraft, it would be more likely to be found than anything else he disposed of or even his own body assuming he was a no-pull.