I have some old packages on a shelf and have used them and once they get wet from wiping up something or wiping your hands they have a bad stench. Maybe that is why I have left them on the shelf. The stench stays on your hands.
It's weird because i know exactly what smell you're talking about but the ones i have now don't smell like that. It's almost like it comes and goes. I'm not sure what it is! They do work so much better than other paper towels though so i deal with it.