Yes, dialysis is surprisingly good at filtering out viral particles, but... that's not desirable in this case. After all these viruses are carrying the therapeutic payload, if you filter them out then you might as well not introduce them in the first place.
Ok, I was thinking more of injecting viruses upstream, and filtering them out downstream (preventing them from entering the liver in the first place). Maybe you could even recycle them.
I suppose it's possible at that point, possibly to try and stem the process. The question is just how rapidly this condition emerges, and I suspect (although this is just a suspicion) that the time between onset and a severe reaction is fairly brief. Mostly though the problem is that this is a really complex, whole immune system reaction that's triggered by the AAV in the liver, but simply removing the intial cause probably wouldn't stop the cascade.
I took a look at some of the aftermath reports (i.e. https://pmc.ncbi.nlm.nih.gov/articles/PMC10638066/ and some others) which get into specific details about the course of treatment in several patients who died from this complication. The through-line is an aggressive use of several immune suppressing and modulating therapies to calm the cascade.
I have to admit I can't find any specific discussion about dialysis in that context, so I can only assume that removal of the viral particles would be a case of closing the barn door after the horse escaped.
