The Taliban and al Qaeda are almost completely linked in Afghanistan today, and the people with the British dog are therefore terrorists. There should be no question as to whether action should be taken against the people who have the dog - the only question is how severe it should be.
Yes, NATO should force the Taliban to return a dog to British custody, because they are only keeping it as a symbol of something that they took from the opposing forces. It is no different than taking a prisoner of war. It is unfair and an act of war to keep the dog, knowing what it symbolizes.
In reality, NATO shouldn't and really can't force the Taliban to return a captured dog to the British. The fact of the matter is that NATO has no standing and couldn't force the Taliban to do anything. The organization could negotiate the return of the dog to the British, though.
Alright, now this is certainly the height of complete ridiculousness, and a waste of vital government resources. With all the suffering that's going on requiring NATO involvement in areas where the Taliban operates, there is no reason for them to waste a single thought over someone's dog. If you don't want Fluffy in harm's way, don't take him into a war zone!
I do not think that NATO should focus on things like that. I don't think that NATO should force the Taliban to return a dog to British custody. I don't think that NATO can force the Taliban to do anything, so by attempting to force them, NATO might just be causing a problem.