There's no fix. Support answered my ticket and the only solution they proposed was send them my phone to further investigation and receive a replace (I guess, it was not so clear). As my former Nexus 4 died abruptedly and I was left with only my FP2, I could not send it, because I needed it.
Using my FP2 daily I merely see the bug nowadays, because I don't power it off. As I mentioned, the bug occurs to me almost only just before booting up.
I still think is a hardware issue with the connectors (pins) between the screen module and the chasis. I sometimes (once in a while) observe a little lag in the bottom left "squares" when swiping over my RSS Reader. Not a very big problem, but for a 550€ phone, that shouldn't happen… it is one of the multiple polish reasons I'm not recommending to buy an FP2 (although I'm still supporting Fairphone).