You might want to surrender Disembarkation card. Disembarakation is also not asked, but you have to surrender so that when you return their database shows that you left America. I don't know about green card holders, but I know others have to do it. I guess green card holders also have a cap time that you can remain outside USA, and in that case, you might need to update your information in immigration USCIS by telling them your departure date, and it is via the disembarkation card. Unlike to other countries, US immigration is absent at departure lounge. So, it should be volunteer surrender. If you have disembarkation card that is with you, it would better to find ways to surrender or pass it to USCIS. Though I am talking RAW talk. Good Luck. GP