To be completely honest, by the time Hana named herself it was kind of obvious that the SI part of the story was kind of... not. I suppose that what I am trying to say is that Hana treats it like it is: a general knowledge download from some random person in another dimension. She never seemed to identify herself with that person's memories, and ultimately her choice to name herself Hana Teiwaz (rather than simply give the name associated with those memories, which in fact never occurs to her) is a clear statement that she considers herself a separate person from the source of those memories.
That said, I don't see any need to change the fact that she has those memories. Between the Chozo's experiments regarding phazon, and the accessing of minds from other dimensions in the Surge Concerto series, it leaves her origins vague but clearly experimental without violating the... physics? Cosmology? The setting? And frankly, if Hana didn't have those memories, she would just be really confused at the start, have no idea what she is doing, and would honestly probably not come up with the ice spear spell (due to not having metaknowledge that metroids have an ice weakness). This would probably mean she would just avoid the metroids completely, and you would have a hard time justifying her finding her way to the Chozo ruins.
That's not to say that you can't rework it. Having database information on the Fleet of Fog, EXA_PICO, and the Chozo could account for pretty much everything if you are clever. But then any gaps in Hana's knowledge would be hilariously suspicious (so I know all of this, but not who made me and why?) unless you are careful. If you go too another way, you would kind of fizzle out the plotline of Hana's quest for identity and her issues with not knowing about her abilities and needs.
I suppose that what I'm saying is that I would favor letting the SI portion fall by the wayside as you continue and develop Hana as her own character, but I don't think that you should necessarily go back and expunge it from the story all together.