I know your comment is in jest, but no, developed countries don't owe developing countries shit.

Well actually, current developed countries owe developing countries for not paying for the externalities (pollution primarily) now causing climate change that were not paid for by the developed countries while they became developed.

That's a purely economic argument and leaves out the exploitation of developing countries by government supported corporate entities over the entire period of colonization.

So actually, you're right, they "don't owe [them] shit." What they owe them is getting rid of the shit that was created in the first place.