In a regular analysis here on LW of Newcomb's problem, TDT receives an unfair advantage, in that it is given this knowledge while CDT is not, presumably because CDT cannot represent it.

The comparison doesn't necessarily have to be fair, it only needs to accurately discern the fittest. A cat, for example, won't even notice that an IQ test is presented before it, but that doesn't mean that we have to make adjustments, that the conclusion is incorrect.

If it means drawing causal arrows backwards in time, so what?

Updates are propagated in both directions, so you draw causal arrows only forwards in time, just don't sever this particular arrow during standard graph surgery on a standard-ish causal graph, so that knowledge about your decision tells you something about its origins in the past, and then about the other effects of those origins on the present. But CDT is too stubborn to do that, and a re-educated CDT is not a CDT anymore, it's half-way towards becoming a TDT.