Comment by Slartie

Europe has banking, too. Even better: nobody in Europe sends paper checks around anymore, we use instant wire transfers here! European banking is way ahead of US banking in a lot of ways.

So, banking is not exactly something that the US can use to coerce a European company. There are much more effective avenues for coercion, though. But IIRC, in this case, the US gov basically convinced the Dutch gov that making ASML adhere to US restrictions would be in the best interest of both of them, and not much coercion was necessary. After all, both countries are on the same side when it comes to the system conflict with China.