Don't worry. Going in, Argentina won't ask for anything US related, just your passport. You will have to show your documents (GC + extension letter) at the counter in Argentina when you are going back to the US so it's the airline folks looking at your documents, not Argentinian officers. I did this in 2019 in Chile (flew LATAM) and no issues whatsoever. I did it as well in China and had no issues either.