Hello, my name is***** and I have over 20 years of experience as a veterinarian. I understand that you are concerned about your pups eating a handful of shelled walnuts.
Walnuts themselves are not toxic for dogs. If they chewed them then they should be able to pass. Walnuts have a bad reputation of making dogs sick, but that is because they can grow a particular type of mold and can get rancid if left in the shell and allowed to get wet, and that can make dogs sick. In this case the nuts were shelled and not moldy, so they should not be a problem.
Nuts in general are a little hard to digest, and they have higher levels of fat then dogs should eat so they may have some mild stomach upset from that. If they seem at all like they have an upset stomach then you can feed a bland diet for a few days.
A homemade bland diet consists of 1/3 boiled, lean hamburger (or boiled, white skinless chicken), all fats and juices drained off the meat, mixed with 2/3 boiled, plain white rice. Add warmed low salt chicken or beef broth to get additional fluids into them and make the food more palatable. Feed several small meals a day for a few days and then once they seem back to themselves transition them slowly back to their regular diet.
Your pups should be fine, please let me know if you have any further questions.