I was having the same problem and ended up removing the "Lux" app I was using that would automatically adjust my screen brightness. The following solution was from another web site which had me looking at that app which was causing my screen overlay problem. I don't remember the persons name who originally posted the following solution but I'd like to say thanks and I hope it can help you figure out your problem.
Friendly PSA for those upgrading to Marshmallow that use Twilight or a similar app to adjust their phones background lighting.
It seems that apps (or at the least I can confirm this with Twilight) that apply any kind of filter to your screen WILL be detected as having an "overlay"
Meaning, you cannot edit any app permissions with them active. You have to pause or disable Twilight so that it is no longer applying the filter in order to be able to edit app permissions in 6.0. Otherwise, you'll just get the "Screen overlay detected" message and be lead to confusion when you can't figure out why. Pause any kind of app like that and try again, should no longer be a problem then.
For example, I just recently installed skype, in order to allow skype camera permissions, Twilight had to be paused.
Chainfire's CF.lumen causes the same issue, although I've never seen a "Screen overlay detected" message.