They can certainly close it, which only initially requires that Lloyds substantially raise their rates.
That said, they can't keep it closed very long, but shy of invading Iran, they could continue to launch shore based anti-ship missiles at will.
The biggest reason why they won't, is that they will be hurt worse than anyone else by a closure.
Yes people forget Iran has to export also. I think they have a big export terminal out in the middle of the Gulf on Karg Island which we could basically turn into silly putty. We bombed the stew out of it last time around. Plus we could just totally destroy their navy in a day. They have some silkworms that would be worrisome but the price they would pay to blow off a few missiles would be too devastating. They are just pulling our tail because they know the muzzie lovin commie in the White Hut will put up with it. Jimmah Carter redux.
The late Shah built at least one oil loading capable port in South Iran,(Mahshahr?) which does not need tankers to pass through the Straits of Hormoz and oil from nearby, main oilfields in Khuzestan, South Iran, already has some pipelines operational.
I am not sure if the Mullahs have kept the port capability up to “code”. There were reports that tanker loading was way below original capacity in the good old days of the Shah.
Danger to Iran is not oil export, though it would be reduced, but a total oblitaration reaction from the West - or if Obambi sits on his hands as before, a strike by Israel.
Closing the Straits needs only the intentional, or accidentally on purpose, sinking BY FLOODING THE BILGES - of some otherwise useless rust bucket cargo ships, even an old tanker or two, to make the Straits too hazardous or “un-navigable” rather than a military exchange sinking naval vessels.
Like when making artificial reefs to protect/increase certain fish populations. Removing the wrecks will take time and enormous effort. And not a single shot would have been fired by Iran.
In all probability Iran would accuse Israel and the West for such events and pretend innocence for their own sabotage of the navigable channel.