Questions of conscience are questions that a person asks because he wants to know if something is sinful or not. In this case, a person might ask if the food at the market was offered to idols; if he thinks that it is sinful to eat food sacrificed to idols, he would feel guilty about eating it. Paul is saying that the person does not need to ask if the food has been sacrificed to an idol or not. Alternate translation: "without asking questions that could make the conscience feel guilty" or "without asking questions about whether it is sinful to eat it" (See: [[rc://en/ta/man/jit/figs-explicit]])