Yeah i thought they did that too, seems they didn't probably because they'd be breaking the Argentine law by driving with the wrong number plates on the car they brought over. They did have the old H1 VAE number plates that the owner uses on his new Porsche (i presume that its the same owner) but i'm not sure the regulations about changing the registration whilst in another country. They did break this law as you can see when the car was stoned they had the H1 VAE plates on it. So it seems they changed them in Ushuaia.
I've a few friends who are fans of the show and mentioned they were coming over, They sent pictures of the cars parked in Patagonia saying how nice the scenery was, they didn't see any association of the plate with the Falklands until all the bull shit started.
There is actually a car blog in Argentina that was following them and posting pictures of the Top Gear team before the plate was noticed. There were some 100+ comments from Argentines not one noticed the license plate, they were just either pleased to see Top Gear in Argentina or checking out the cars theyd brought with them.
Regarding the swapped plates, they must have changed the plate when in the hotel in Usuahia when they were told to leave, which kind of points the finger at the Top Gear team for saying it had been changed before they arrived in the city when they were told of the issue.
Anyway, it was all good publicity for Top Gear, and bad publicity for Argentina. Which was a shame, as they said on the film before the end Tierra del Fuego is the most beautiful place theyd ever been too.