Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am sorry to hear that your pups got into mischief and were chewing on and possibly ingested some of an ageless oxygen absorber packet. This product contains two active ingredients, calcined which is a silica (like sand), and iron oxide.
Neither one of these is truly toxic, and I suspect that the product has to labeled "DO NOT EAT" simply to indicate that this isn't food. Silica absorbs water, and can be a mild gastrointestinal irritant if eaten in sufficient quantities, but I suspect there isn't enough in this packet to cause a problem.
Iron can be toxic if eaten in significant quantities and in an absorb-able form, but iron oxide is a form that is poorly absorbed in the digestive tract, thus is not the form we need to be concerned about. This can be a gastrointestinal irritant as well, but is not truly toxic.
If the package were swallowed whole the cloth-like material and absorptive properties of the product could lead to a gastrointestinal blockage, but it sounds like your pups had torn the cloth covering apart and ingested some of the contents, and so they should be fine.
In short your pups may have mild stomach upset (some vomiting or a decreased appetite), but that should be it. And if they only ate a small amount you may see no symptoms at all.