I saw this idea on the reddit page here, and I wanted to elaborate (stop me if you heard this one before on this forum).
At first I thought it was a long shot, but I was rereading earlier and I think that it's true. Obviously because of the the reasons mentioned in this post referring to with the background pic in ch 4 pg 35. One commenter on the reddit page also mentioned the flashback in ch 4 pg 112, where Max's friends' mom (or possibly aunt, or cousin) has a similar body type and her face is cast in shadow.
There are also ch 4 pg 135, where he looks at her like he's seen a ghost (lol), ch 4 pg 141 where he's staring intently at her like he's trying to figure something out, and ch 5 pg 25 where he lists off all the random facts about her.
So. Max knows Agent Day as his friends' mom/aunt/cousin/relative.
He doesn't bring this up to her, though. We know Max as a character who plays his cards closer to his vest, and he probably wouldn't want to bring this up in front of Spender and the rest of the Activity Club, anyway, and he hasn't had the opportunity this far into the story to try and speak to her privately. But there could be another reason he doesn't try to talk to her, and that ties into the fact that she doesn't recognize him.
Yes, she's blind. But one would think that she could be able to recognize the sound of his voice, since he was such good friends with her (supposed) kids/niblings/cousins. At least, she should recognize his name when he's addressed by Spender and Isabel when they meet up in front of the train. She doesn't, though.
My theory is that Day lost her memory somehow in some kind of accident that also made her lose her eyesight and also made her a spectral. Three in one.
In ch 4 pg 65, Spender refers to Day as a low-level spectral and also Walker's pupil, which insinuates that, while she's an active member of the Consortium, she's still possibly learning. Since Max's mom died five years prior to Max's family moving to Mayview, this gives Day plenty of time to learn about Paranatural activity, learn about being a spectral, and become a member of the Consortium. This timeline can at least still accommodate the idea that Max knows her.
It also gives her enough time to recover from losing her eyesight in some kind of near-death experience, which turned her into a spectral. Somehow, she stumbled across a cane that was also a tool.
The loss of memory and sudden blindness means she spends less time with the twins (I'm starting to warm up more to the idea that she's more of a cousin or aunt than their mom), but invests her time in the Consortium and learning to be a Spectral, especially since her tool is her cane, and can help her to interact with and "see" the world in more ways that one.
And that's what I have so far. As a first post, I hope its okay