No! It means 'keep (the errant creature) under control', as 'curb' means 'control' (from French 'courber', which is a verb). Stop it from doing what is left discretely unspoken, as being unspeakable anyway.
The kerb is there to separate road traffic from that on the pavement, except in Bangkok where anything goes, really. Dogs just lie there, supine and quite pointless. And no one would tell anyone to do anything with his dog, as that too would be pointless, and most impolite. I have mentioned earlier that in England no one would do so either, as it would provoke outrage.

No, no, no. If 'curb your dog' meant 'steer it towards the kerb to do its (ahem) business' you would cry out "kerb your dog". If you mean 'stop it yapping' or 'stop it sniffing the genitalia of folk standing there quietly' you might call out "curb your dog", but in England it would make no difference as it sounds much the same and in England dogs rank higher than humans anyway, and the owners would be mystified.

I think that the "curb your dog" means "restrain your dog" which may include when you spot the errant pooch laying a turd in the street. It has nothing to do with the kerb, which is indeed the raised bit for pedestrians (and in Bangkok the motorbikes and bicycles) next to the road, which is for cars and lorries and buses (and in Bangkok the pedestrians). In the USA this is called the 'sidewalk', in English-speaking countries the pavement. Actually, I think the kerb is the part of the pavement next to the road, not the whole thing.
In England, where dogs are treated in the same way cats were in ancient Egypt, to tell someone to "curb your dog" results in cries of anger and threats of violence, and not from the dog but from its owner and also bystanders who do not know you from Adam. A more subtle approach is to pick up the offending faecal matter, run after the dog's owner and give it to him, or her, and say "your dog dropped this".
'Curb' is a verb, 'kerb' a noun .

Well, I think it's funny. I associate it with slow-speaking women customers of a certain age in Dorset and Devonian pubs making snide comments to their menfolk (whom they seem to wish wouldn't make them come to these places) about the cleanliness of the facilities, but asserting by way of a coda that they are just sayin'. As it is clear that they are just sayin', there is no need really to explain so, is there? That's a bit of what I find funny. But after a few pints of the marvellous real ales to be had in South-West England almost anything seems funny. Cheers! Just sayin'.

Don't worry about it, Jayles. No need for conturbation on your part. Your remarks at 6.05 pm please me greatly, as I am sure they do all of us.

Indeed, Jayles. Quite so.

Sundy,
you are too kind about my English. In fact, would you believe, my first language was Zulu, so there is a bit of doubt about whether or not I am a native speaker of English. No, I was never taught the English subjunctive by any English teacher. In Britain English teachers do not really teach English at all, but rather creative writing and poetry and drama and nice things like that. Grammar is not taught, as incredible though this may sound, it seen as elitist, I am told.
Now, where learning English properly is best done is in the Latin classroom, where that language is used primarily as a tool through which proper, grammatical English (or indeed German, French, Italian, whatever ...) may be studied. The study of modern languages is different: its purpose is to learn that other language. So those who study Latin even to a fairly elementary level understand grammar, including therefore the grammar of their own languages. And that is where I learned my grammar, and taught it. I am told by others that you can tell in less than a minute, from his speech patterns, if someone has learned Latin, and I take their word for it. I always assume everyone has learned it.
This forum has provided me with rich food for thought and entertainment beyond the limited linguistic playing fields of those happy schooldays, and I especially enjoy the fancy terms they have invented to keep us busy, my favourite today being Irrealis, the unreal past. Love the capital I ! Which institution cooked it up? Cambridge, I see. Latin, yes, good, but why the capital I? I'm an Oxford man myself, and we called it the unreal past. Well, we would have done, but actually we never spoke of it at all.

Sundy
You rewrite my sentence by scattering a few commas around in it: "the subjunctive is the ultimate polish, which, once mastered, allows the user the right finally to claim that he has learned the language."

You say "to be honest, it's a bit complicated sentence".

Yes. Is that a problem?

'A bit complicated' does not work well here as an adjective describing 'sentence', does it? "This sentence is a bit complicated" is fine.

I agree that matters such as the use of 'that' when you mean 'which' or even worse 'who/whom' need attention too, as of course do dozens of other fine points, but they need only a few lines each of explanation in a language course, whereas the subjunctive is, as the conversation above indicates, complex and not to be covered in too much hurry.

Sundy, you miss my point about the fact that there is at least one prime minister in our recent history who developed dementia and may well at times have not been aware that he (or indeed she) had once been prime minister, and at more lucid moments would be in a position to advise others that this honour had once been his, or hers. Telling people things which they must surely already know ("I used to be prime minister, you know") is perhaps a rather obvious consequence of dementia. To assert then that "if I was prime minister" is a possible open condition, one which the speaker does not feel able to assert is the case, nor not the case, but must let lie open, is a perfectly feasible possibility. Nothing weird about it, this unhappy condition happens to people, prime ministers included.

You allow that I could give (you) poor marks of English (sic), and indeed I I fear I must. But keep cracking away; the subjunctive is the ultimate polish which once mastered allows the user the right finally to claim that he has learned the language. Oh yes, and those pesky prepositions too.

You say you would be very nervous if I were to say that “I accept it is possible that I was prime minister at one time, but I can't remember”.
You are evidently of a very delicate disposition. A past prime minister of Britain in the last fifty years did indeed develop dementia, in more lucid moments telling other people "I used to be prime minister, you know". Those to whom he confided this information did not report feeling nervous because of it. Nor did they call the police to take him to hospital for an overall medical checkup, as there was no need for one and in Britain the police are the wrong agency for this. As you point out you can’t forget if you were once the prime minister some time ago unless there is a medical problem, so this is not an usual context. Well, Sundy, it may not be usual for someone to develop dementia but it happens.
Besides all that, the point under discussion is a linguistic one.
On another linguistic point, what does this mean: "You are kind of trust your girl friend on that she wouldn’t do this ... "? You wrote it. No need to call the police, but it scores poor marks for English, I feel.