The ''thank you'' is merely another command or release word for the dog to associate. It is, in another way, a different way to train the dog to stop barking on cue. Many people train their dogs to stop barking by first training them to bark on que, so they can then train them to stop on cue as well. This "thank you" concept is much the same conditioning and association work.
Basically you are letting the dog know with the sound "thank you" that his guarding/barking job is finished. Just as one releases a dog from a stay, you are releasing the dog from his "duty" to warn you of something going on you need to attend to.
Now, this doesn't mean that you just have to yell "thank you Spot," from the living room and expect the dog to stop barking. You also need to then take the Alpha role and check out what the dog is trying to tell you. Thusly, you let the dog know (i) his warning job is finished and he's done a good job (praise and reward), and that you, as Alpha of the pack, will take over from here and protect the pack and territory. It releases the dog from that responsibility and his barking as well.
Yes, the dog doesn 't understand English, but he makes associations with sounds (the sound he hears when you say "sit") to certain behaviors. This is the same thing. I thought it odd too when I started with my dogs to think they'd understand what "thank you" meant. But, oddly, the very first time I tried it, they stopped barking! I was stunned. And it has worked every time from then on with my two boxer girls.
I do go and check it out, from time to time, and other noises, which I recognize, I ignore and call the dogs to me after thanking them, and praise them and engage them in something else, breaking the focus on the "noise" which caused them to bark in the first place, letting them know they have done a good job but it is over now and that that particular noise is of no concern to me and shouldn't be to them. In this way, I have also had success in getting my dogs accustomed to certain sounds outside which occur frequently (car doors slamming, etc.,) which used to cause them to bark, but now they ignore as just any other noise they are accustomed to hearing a lot (cars driving by, sirens, etc.).
Hope this helps in clearing this up for you.
Have you read Jan Fennell's newest book "The Practical Dog Listener?" It clears up a lot of the questions that people have about her technique and gives you a day by day schedule on how to put her techniques to work for you and your dog(s). Might want to check it out. I found it very valuable in addition to Dog Listener, even tho the same material was covered. Just more detail and further explanation in the second book.