In ''Simon Says', Gabriel definitely has a unique interest in Cat Noir's and Ladybug's Miraculouses.
And as Hawk Moth, he even says 'it will be risky. ' when he knows about Simon Says plan to get a hold of Gabriel Agreste. Why so?
Uhhh duh? Becuz he is wondering about the reputation of Gabriel?
This might sound crazy, but I think the painting of Gabriel's wife is the secret entrance to the place where we often see Hawk Moth: the circular room where he releases his akumas.
You can see that her photo was the only one in the whole room not to be thrown on the floor. Perhaps it is because the minions of Simon Says couldn't? Perhaps it was permanently stuck to the wall as a back door to Hawk Moths secret hideout? After all, who in Paris would have enough money to own (That I presume, since we always sees Hawk Moth there, certainly he owns the place?) a building high enough to survey all of Paris?
Also, we see a lot of Adrien's mother in this episode, alongside with Gabriel's strange interest in the superheroes Miraculouses.
Maybe it is foreshadow for us to understand the true reason why Hawk Moth wants the Miraculouses so much: he wants to bring back his wife, (I can't remember her name sorry).
Idk, this is all just a thought.