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I would like to help you and your dog with this question, but need a bit more information in order to better assist you.
These bits of plastic could become a Gastrointestinal Foreign Body.
Dogs eat the strangest things - plastic bags, children's toys, bones, bits of towel, socks, rocks and other things. Often, these foreign bodies pass through the intestinal tract, but sometimes they do not. They may get caught in the stomach or the small intestines.
The symptoms of a GI foreign body are generally vomiting, loss of appetite, depression and dehydration.
In the case of an obstruction, surgery is often needed to remove the foreign object.
I will include further information about GI foreign bodies:
So, we definitely want to avoid this!
It would be a very good idea to provide your dog with safe things to chew on, in order to redirect his instinct to do this.
Good options are:
1. Kong toy
This toy is (almost) indestructible. I have found that dogs particularly like it if you put a little smear of peanut butter or cream cheese at the bottom, or freeze some chicken broth in the bottom.
2. Rope toys
Many dogs love these - particularly if you soak them in broth and freeze them. You do have to replace them when the dog begins to shred them as swallowing sections of rope can also be dangerous.
Both of the above are safe for their teeth and good for redirecting this chewing behaviour!
I hope that helps!
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.