It isn't just a question of whether or not they would want to wear the insignia of the 106th because it could be considered a "hard luck outfit" - there is also the question whether the personel of the 159th would say amongst themselves - "hey, we're Guardsmen from California, the 40th Division no matter where they send us". Of course I don't know how many original guardsmen were left by 1945 - perhaps it was simply stripped of its original personel over the years and just filled up with replacements. (The 28th Division from Pa was stripped without mercy)
Another aspect is that in combat brightly colored patches aren't neccessarily a good idea - many were removed by troops from their outer clothing.
He may have had the patch simply because that is what was worn when his unit was attached to the 106th. Interesting though is that unless the 159th had its own sleeve insignia authorized - had he reentered the Army/National Guard/Reserves he would have probably worn the 106th SI on his right sleeve.