Regardless, I could see Walt coming up with some contrived account like; he some how met Gael or was introduced to Gael, who wanted to pick his brain about some chemistry processes for something he was working on or related to his Masters thesis or even a PhD project he was contemplating. The way Walt so often feigns tears, he could claim he was too scared to say anything when Hank showed him the notebook for fear he would be implicated. Remember after having too much wine at dinner one night, he told Hank the notes in the notebook looked like copying, as he had seen plenty of student's notes, after Hank's gushing over Gael's genius finally got to his ego. He could claim the "work" was simply instructing Gael on particular chemical processes that could be used in many applications, although he "pondered" whether it could be for meth synthesis or “something illegal". He was just so caught up in the mental challenge of solving this chemistry project and flattered at being so respected for his expertise, especially with the looming cancer diagnosis making him feel like he had wasted his talents. So he got carried away with “helping” Gael figure out his chemistry dilemma, even though he had concerns that his coaching could be getting him too involved in “something” he shouldn't be doing!

I could see him coming up with an elaborate fabrication like that to explain his association with Gael, as implied by the note in the book. Hank won't believe it but it could be a plausible explanation that Hank probably couldn’t prove otherwise . . . although there is the “gambling” money. Also, referring to the comment about Walt being family and right under Hank's nose, once it comes to light that Walt's money paid for his therapy, Hank might decide he likes Walt's fairytale version. At any rate it’s fun to speculate on the various scenarios that might play out.