The delayed choice quantum eraser is misunderstood (even by PBS Spacetime) to invoke time travel/retrocausality. The truth is that the pattern seen on the screen is the same whichever set of detectors you send it to, and as such, there is no evidence of time travel.
The more plausible explanation behind the delayed choice quantum eraser involves Heisenberg's Uncertainty Principle, which states that you cannot obtain position and momentum to a high degree of accuracy at the same time. Einstein's EPR paradox "proved" quantum physics incorrect by setting the Uncertainty Principle against Entanglement. He did this by a thought experiment that entangled two particles, and measuring the position of one and the momentum of the other to thwart the Uncertainty Principle.
The delayed quantum choice eraser is a realization of Einstein's thought experiment. However, what Einstein didn't realize was that while the standard double slit experiment produces a pattern at the screen that gives you the momentum information, entangling two particles creates a different pattern at the screen that causes the particles by themselves to give neither momentum nor position information. The delayed quantum choice eraser initially recovers the position information by combining information from both particles, but by choosing the other set of detectors you can "give up" that information to gain the momentum information. Either way, you are still unable to obtain both pieces of information at the same time.
Source: I am writing a book on Quantum Physics and have spent months doing research and finding out that even many quantum physics Youtubers routinely say misinformation. By far the worst is the incorrect idea that a which-way detector on the double slit experiment will produce two bands as if the particles are marble-like. It doesn't, it destroys the interference pattern, producing a single slit pattern. This sounds like a minor detail, but it contains the realization that quantum physics particles ALWAYS act like waves, even after a measurement, and wave-particle duality is a misnomer.