I agree with Feltwad that the trigger guard is of an older pattern, but I don't see that this is terribly important. I don't even feel that it must represent "old stock" but more that the export market was not as style driven as the British domestic market, or that the styles in vogue with American buyers were often out of date by British domestic standards. Remember, these guns were imported in large quantities - usually several hundred at a time and shipments of more than 2,000 guns are known.
I wonder how important a trigger guard finial was to the ultimate buyer - probably nowhere near as important as having a "roller lock." In American advertisements for loose gun locks, the presence of a "roller" is the only physical feature that is consistently mentioned. Ads will say "locks with and without rollers." It was a measure of better quality. Roller locks always have external bridles and probably always have internal ones as well, at least I've never seen one that had the external bridle but lacked the internal one. Export locks without rollers often lack both although I can say with certainty (from a primary document in my possession) that a large variety of locks were offered, including with waterproof pans and sliding safeties. How many were sold is another question - one I can't answer.
As for the TB mark, I suspect that someone with the patience to check all Birmingham gun barrel makers in the right time frame would likely come up with one, maybe even more than one, with those initials. For my own part, I have reservations about it being the barrel maker's mark. Where these are readily recognized they are usually on the underside of the barrel - the mark on the top of the barrel is usually that of the "gunmaker." In an earlier time frame, in London around and before 1750, this was often the only place the maker identified himself. Actually engraving the makers name on the barrel or lock is a later convention. I see no reason to presume some makers didn't keep doing things the old way, especially when making guns for export where the customer (the American dealer) may not have even wanted the name of the maker displayed prominently. "London Warranted" only says its an English lock. Almost all locks were English so this wouldn't compromise an American dealer who wanted to imply he was the maker.