My dogs have eaten worse, the dog may become distressed if the string comes out as a long length, the anal muscles will contract, the best way to deal with this is to make the dog calm and gently pull the string with an even pull, do not force it, the calmer the dog the better the procedure, if the dog gets very irratated then always consult a vet.
The string will come out on its own in most cases. There can be problems if it does not come out, it will not digest and can in extreme cases cause blockages, its rare but possible.
Anyway Patch will give you the proper info when he sees this post.