Comment by Animats

That issue came up regarding China's Confucius Institutes.[1] There's been something of a crackdown on those.

Politico has some coverage of the current Israel-related lobbying push.[2] There are a lot of players. "An unsanctioned coterie of pro-Israel quasi-lobbyists has descended on D.C." Some have formally registered as agents of Israel. Some haven't.

The big issue here is when activities go beyond lobbying. Anyone can lobby Congress; that's a constitutional right in the US. Getting people fired on behalf of a foreign power, though, is a legally questionable activity.

[1] https://thediplomat.com/2023/11/the-rise-and-fall-of-confuci...

[2] https://www.politico.com/news/2023/10/22/pro-israel-lobbying...