That's not the case, actually. The languages of the Iroquois don't make a distinction between the K and hard G sounds (nor between T and D), and so their official writing systems often don't either. When they do, they're reflecting a difference in pronunciation that is present but not distinctive, like how the P in "pit" is pronounced with a puff of air but the one in "spit" isn't, but English speakers still consider them to be the same sound.Yes, exactly!
As for the difference between the usage of K and G, I'm not entirely sure, but I think that it's the difference between a hard sound and a soft sound. So like, the G in "Gram" vs the G in "Gentlemen", and I think that the K is used for the former.