shut it down

Now when they saw the boldness of Peter and John, and perceived that they were uneducated, common men, they were astonished. And they recognized that they had been with Jesus. But seeing the man who was healed standing beside them, they had nothing to say in opposition. But when they had commanded them to leave the council, they conferred with one another, saying, “What shall we do with these men? For that a notable sign has been performed through them is evident to all the inhabitants of Jerusalem, and we cannot deny it. But in order that it may spread no further among the people, let us warn them to speak no more to anyone in this name.” So they called them and charged them not to speak or teach at all in the name of Jesus. But Peter and John answered them, “Whether it is right in the sight of God to listen to you rather than to God, you must judge, for we cannot but speak of what we have seen and heard.” And when they had further threatened them, they let them go, finding no way to punish them, because of the people, for all were praising God for what had happened. For the man on whom this sign of healing was performed was more than forty years old. (Acts 4:13-22, ESV)

The HS had given them boldness to speak about Jesus in the face of opposition and that was noticeable to the authorities. There was nothing special about Peter and John, the difference was that they had been with Jesus.

The authorities recognised that they could not deny the miracle, but they were desperate to shut down the message. "Sadly, the leaders were motivated by fear of losing power and influence rather than by a desire to glorify God, to be faithful to his Word, or to spread the true knowledge of salvation." ESV study bible

The disciple's boldness continued - they recognised that their was a limit to their obedience to human authorities, and that limit was reached when their instructions conflicted with God's.