the executive branch does foreign affairs. the house of reps does not. i used to live in taiwan. foreigners are prohibited by taiwan law from participation in taiwan politics, period. when US house members travel abroad they do so as private citizens and all they say/do is as private citizens. bay in the day when hastert (?) did a similar trip every news article covering his trip always include the disclaimer that he was on a trip as a private citizen and he has no authority to engage in talks with foreign entities.
serious question: why can't states that need workers sign up to receive new comers? ya know, if New York State figures it needs 100K folks then folks are sent there?