Is it necessary to remove oils or creams mixed with ritual impurity from the body, even if the impurity has been removed and only the trace of the oil or cream remains?

The criterion is the removal of the impurity. If the impurity is removed, then the persistence of the trace of oil or stickiness on the skin does not matter. We advise against indulging in these thoughts, for they are from the whispers (of Satan/waswas).