Miles figured that the polite thing to do would be to offer to carry on helping Charlie and Billie, but he also kind of wanted to go back and hang out with his friends rather than spend his evening with a stranger and a dog that didn't belong to either of them. "I'll sacrifice the scarf," he decided, since as nice as the scarf might be, it seemed a bit unnecessary for Charlie to come back looking for Miles. "Or you can tell the owner to owl it back to me if they'd like, my surname's Bletchley," he added, since that way at least it wouldn't be an extra task for Charlie. "It would also be nice to hear if she got home safe," he admitted.
Handing the dog over to Charlie and more politely than sincerely asking if Charlie was sure he didn't want Miles to stick around, Miles bid his farewell to both before going off to find his friends and rejoin them.