The Trump supporters have some really twisted interpretation of the Green Climate Fund, which they seem to read as the United States having to give away tens of billions of money to poor countries.

That's not at all the case. The GCF is rather analogous to the something like the International Monetary Fund (IMF), which mostly has been a tool for powerful countries like the United States to be able to influence smaller countires into using their economic system - just that his is for climate rather than economy. The GCF won't just give money away, they'll provide more advantageous loans to poor countries to allow them to develop green infrastructure that is more expensive in the short term, rather than dirty infrastructure that is cheap in the short term but expensive in the long term. The US would provide a non-unsignifcant part of the money as the world's largest economy (and a big polluter), but let's repeat something again: the fund is going to give out loans, not give money away.

But try to get them to understand that...