My experience says the ones that have been through a dryer cycle will have a more open weave that traps the fine tumbling dust better than a new un-used one.
I don't have good access to used dryer sheets since we don't use them for laundry. So my practice is to cut a paper towel into strips and use that instead. It may not work quite as well as the used dryer sheet, but it works pretty well. I put a small amount of mineral spirits on them before I add them to the tumbler. Seems to help capture the dust.
I have also found that while the dryer sheets or paper towels do allow you to extend the media life, there comes a point when I just decide to change it out with new. And every time I do, I always wish I had done it sooner. YMMV