I am sorry to be so late with a reply.
Did your dog pass that piece of cloth safely? If so, did it all come out? Very often they will pass something like that but it depends on what and how much has been swallowed, and sometimes it can cause a serious stomach or intestinal blockage.
The best thing to do if a dog swallows any foreign object is to immediately call a vet on the phone for advice at least. The vet may or may not need to see the dog in a consultation but it's better to get advice quickly.