Imagine if the woman hadn't got the message to Gort, and he went on a total earth-destroying killing spree. Do you think - with our current artillery - it would be possible to actually take him out? What would you use and how?
I'd simply dig a hole and push him into it. Or spray him with water until he rusts and seizes up!
Even KZ69 clear plastic, stronger than steel, couldn't hold him.
The space-age metal alloy that Gort is made of would withstand multiple direct hits by nuclear bombs.
Gort would simply plod along, melting everything in sight with his laser. It would take him a while to destroy the entire earth at the slow pace that he walks -- although I imagine his designers incorporated some ultra-destructive device -- that was not mentioned in the movie -- that would devastate the entire earth in short order.
He has impenetrable armor, so a nuclear blast would probably do nothing to him. He has a laser which can penetrate and evaporate anything, so incasing him would be useless. The one weakness I see is speed. You'd need to propel him into the middle of the ocean. So lure him to walk over a nuke to launch him. At the speed he walks, it'd take him years to get to land again.