What is the ruling on the residue of impurity remaining on clothing after istinja, and what should be done about it?

This is merely a baseless doubt (waswas). Pouring water on the hand after performing istinja' (washing after defecation/urination) is sufficient to remove the traces of impurity. If you are certain that your hand is impure, rubbing it is not enough; rather, you must pour water over it until the impurity is removed. If the color of the impurity remains and it is difficult to remove, then it is excused. Whatever you doubt has become impure, its original state is purity. Whatever you are certain has become impure, you must wash it with water. If the matter is merely a baseless doubt, ignore it and do not pay it any attention.