Delayed choice quantum eraser and changing the past? I've been trying to get my head around the delayed choice quantum eraser experiments (see Kim et al. (1999) and Wiki for details). Many sources online claim that the experiment indicates retrocausality, i.e. that we can change the past. Including this lecture by Professor Karan Barad (see from 26:40 - 29:15), where she states that

...after the atom has already hit the screen and gone through the slits, I can decide whether it has gone through one slit or the other as a particle, or through both slits at once as a wave does...have physicists figured out how to change the past?

Is she right that something strange is happening with temporality? If so, or not, why?
I believe I need to provide context of what I currently understand to make this answer feasible.
This is what I understand (see diagram below): Particles are split into entangled pairs after passing through the two slits. The signal particles (one of the pair), land at D0, whose entangled idler pairs (the other of the pair) have yet to be detected 8 nanoseconds later at either D1, D2, D3, or D4. D3 receives with certainty only particles from one slit, while D4 likewise receives only particles from the other slit. In this case, we have which-slit information and the interference pattern is destroyed, i.e. there is particle behaviour. In D1 and D2, the separated streams from two slits are recombined, obfuscating which slit they came from, and the interference pattern appears, i.e. there is wave behaviour. That D3 and D4 detect no interference is not strange to me, because you have effectively turned a two-slit into a one-slit; you are forcing only one option, of course there is no interference. But D1 and D2 puzzle me, because how can two objects having gone through two effectively single-slits interfere with each other? (Surely they just create two single bands or one big band? Each object must go through BOTH slits in order to create interference.) But anyway, that's not the question.
The question is: Where is retrocausality in all this? D0 records measurements earlier to D1234, sure, but D0 records no interference at all (which also mystifies me, why doesn't it?). D0 needs to be "cross-referenced" with D1234 to produce images of interference or non-interference. So...is the idea that a signal particle already "knows" where it should land on D0, long before its entangled idler particle has actually taken its path? Thus, by removing or introducing the BeamSplitterC AFTER D0 measurement, we can change that measurement? So would we actually see the pixels on the D0 graph magically change when we decide differently about BSc? That's just absurd. Or, is the idea that our decision about BSc was already predetermined at the outset when D0 recorded the measurement? So the particles "knew" what we were going to do? If that's the idea, it's also absurd...
If anybody could enlighten me, I greatly appreciate it.

 A: The results of quantum physics are indeed hard to describe in everyday language, so you get professional scientists talking about quantum eraser experiments as if they changed the past. But they do not. I noticed in the quotation provided in the question, the phrase

"after the atom has already hit the screen and gone through the slits,
I can decide whether it has gone through one slit or the other as a
particle, or through both slits at once as a wave does"

what this statement misses is that an atom is neither a particle nor a wave but a physical entity whose nature and motion is correctly described by quantum mechanics. Quantum mechanics calculates the probability of what an atom will do by summing a set of quantum amplitudes for each contribution. The contributions may include, for example, motion along a path passing through one slit or another. In quantum eraser experiments some other physical property such as an internal spin state or a light field has become entangled with the motional state, and consequently there is "which path" information. The presence or absence of interference is now a property of the complete entangled system, not just one part of it.
The subsequent observations which are sometimes said to have altered what happened in the past do not do that; rather they show what is observed in the present for states of this kind. But it remains true that there is a kind of non-locality in the results of observations on entangled states, as Bell showed. The discussion of quantum eraser and similar results is an attempt to put words on the non-locality to show why it is surprising and not like classical physics. It is indeed surprising, but people's attempts to put it into words have varying degrees of success.
