If we don't follow Nozick in making this assumption -- if we assume that there is backwards causation -- CDT does not "reject the case" at all. If there is backwards causation and CDT has that as an input, then CDT will agree with EDT and recommend taking one box.

I consider CDT with "there is backwards causality" as an input something that isn't CDT anymore; however I doubt disputing definitions is going to get us anywhere and it doesn't seem to be the issue anyway.

The reason is that given no backwards causation (more on that below) and as long as Omega is good enough at predicting, CDT and EDT will recommend different decisions. But both approaches are derived from seemingly innocuous assumptions using good reasoning. And that feature -- deriving a contradiction from apparently safe premisses through apparently safe reasoning -- is what makes something a paradox.

The reason why a CDT agent two-boxes is because Omega makes its prediction based on the fact that the agent is a CDT agent, therefore no money will in the box. The reason why an EDT agent one-boxes is because Omega makes its prediction based on the fact that the agent is an EDT agent, therefore money will in the box. Both decisions are correct.*

This becomes a paradox only if your premise is that a CDT agent and an EDT agent are in the same situation, but if the decision theory of the agent is what Omega bases its prediction on, then they aren't in the same situation.

(*If the EDT agent could two-box, then it should do that; however an EDT agent that has been predicted by Omega to one-box cannot choose to two-box.)