Conscience as in “do you have a conscience” is a term to describe the understanding of morality, even without a written law. It suggests that we have the knowledge of right and wrong within us.
How is it that babies know how to breathe without being taught? Call this what you want, but humans have inbuilt knowledge in order to function and lead good and healthy lives. When our conscience is seared because of rebellion, then such a person starts to lose basic morality and understanding of things that keep the person in good health and a good mental state. Insanity can be the result of straying too fat from this inbuilt knowledge. Denying God is a form of insanity because it is a denial of the most basic reality. It is God who gave us the conscience. It is there to keep as alive, healthy, and to know the difference between right and wrong.
Indeed, when Gentiles, who do not have the Law, do by nature what the Law requires, they are a law to themselves, even though they do not have the Law, since they show that the work of the Law is written on their hearts, their consciences also bearing witness, and their thoughts either accusing or defending them. This will come to pass on that day when God will judge men’s secrets through Christ Jesus, as proclaimed by my gospel.