If it was a flat strip it will pass through Ok. The dangerous ones are the ones with a knot at each end,they are perfect for killing a dog by swelling and sticking in the throat,before you know it the dog is dead.
I would go to the vets just to be certain. Chloe did exactly this, it was about the size of a cricket ball. We freaked out and ran to the vets, they did surgery cos I was so panicked, and 2 hours after she swallowed it, they opened her up and there wasn't any of it left, had all dissolved. I wouldnt worry! Good luck! xxx