I got reminded of this, and it is important enough I’m going to post in both threads that are discussing this topic. When talking to immigration, border patrol, ICE, TSA:
DO NOT LIE
You may be asked questions, you may choose to answer or refuse to answer. There may be consequences to both things. Whatever you choose, though, do not lie. If you don’t want to answer a question, clearly state that you will not answer, but do not give an answer that is a lie.
Staying “silent” (where silent means clearly articulating that you refuse to answer) is a protected right. Lying to a federal agent is a criminal offense, even if the actual thing you’re covering up is not criminal.