Why is that backward system of differential equations become fundamentally more important when the transition rates are unbounded?
From a search of the internet, it appears that, in broad terms, if the transition rates are unbounded the backward equations are easier to solve/can be solved in more cases than the forward equations. However, the mathematics to back this up seems to be far beyond anything that is expected in CT4. So I'd say that statement is included for information only, rather than anything you'd be expected to justify.