Star Trek: Discovery may have just revealed why Spock never mentioned Michael Burnham in his very long, very well-documented life. In Star Trek: Discovery season 2 episode 7, "Light and Shadows" it could be that Spock just doesn’t remember Michael at all. While Star Trek: Discovery has been an excellent steward of Star Trek canon, it’s also taking some very liberal freedoms to the very DNA of the franchise. When news broke that Michael Burnham’s backstory was that she was Spock’s foster sister, fans understandably scratched their heads.
As one of Star Trek’s original characters and arguably its most iconic, Spock’s background had been very well filled out, as had his father and mother’s. Much was made of Spock’s childhood and relationship with Sarek in previous Star Trek TV shows. His backstory was such well-trod ground that it seemed almost blasphemous to retcon it so extensively. While it didn't bode well with fans, the show has taken every opportunity to promise there will be an explanation for Spock’s apparent amnesia regarding now two of his siblings.
Interestingly, "Light and Shadows" might have just introduced an explanation that makes "amnesia" more than just a joke. It’s possible the memory extractor Leland used to “help” Spock caused or will cause enough damage to the Vulcan that he loses memories associated with Michael and/or a significant portion of his childhood. Spock was already exposed to the device in “Light and Shadows” for at least some time before Burnham broke him out at Georgiou’s insistence. It's unlikely that Spock would lose his memories before he and Burnham resolve their issues first.
It’s worth mentioning that it's more than possible that Georgiou was lying about Spock’s predicament to serve her own purposes, and considering Leland seems to be a little more conflicted about his work with Section 31 than Georgiou is, it’s feasible he genuinely meant Spock no harm. But that still doesn’t eliminate the possibility that some kind of neurological disorder or damage will eventually cause Spock to forget his sister. Plus, using a memory sifter on Spock to make him forget his sister seems like something Georgiou is capable of doing just to torture Burnham.
Granted, it would have to be very localized and selective memory loss, damage, and/or manipulation to only affect his experiences with Michael, but that kind of thing isn’t without precedent in Star Trek. There’s one case of Starfleet doing exactly that in the Next Generation episode “Pen Pals”. Dr. Pulaski erases the Enterprise-specific memories of a young girl Data attempts to rescue from a natural disaster, violating the Prime Directive in the process by first communicating with the girl at all, and then bringing her aboard the Enterprise. The Voyager episode “Meld” features the Vulcan Lieutenant Tuvok using a mind meld in an attempt to quell Betazoid crewman Lon Suder’s psychotic tendencies. It doesn’t go very well, but it speaks to the Vulcan ability to manipulate the minds of others with the use of a mind meld. And in the Next Generation episode “Violations”, the Ullians use telepathic memory retrieval to help others recall events with more specificity, and they’re also capable of manipulating and even erasing specific memories, which one of them attempts to do to Deanna Troi to cover up a memory of assault.
However, if Star Trek: Discovery chooses to go this route in an effort to justify the Burnham retcon, there’s a danger it could feel like a band-aid solution and wind up drawing more attention to her awkward insertion into Spock’s family. Unless executed properly, erasing Spock’s memories to explain why he never mentioned a foster sister at any point during the Original Series, the Next Generation, or the films has the potential to backfire if it feels like a deus ex machina. Keeping that in mind, offering any explanation for Burnham’s curious place in Spock’s backstory could be more trouble than it’s worth if it’s handled poorly and further alienates fans who still protest her existence in the first place.