Looking at your phone screen in the dark could damage your eyes.
But looking at the phone screen in the daylight or in a well lit room should do no harm to your eyes.
Looking at the phone screen in the daylight should do no more harm to your eyes than looking at a TV or computer screen.
But it can be bad for your eyes to look at your phone screen in the dark or in a badly lit room just like it can be bad to look at a computer screen or TV in a badly lit room.
I know some people that like to watch movies with the lights turned way down but it gives me headaches when I try to watch TV with the lights turned down.
So for me it would be bad for my eyes to watch TV with the lights turned down so looking at a phone screen can be damaging to your eyes and give you headaches when you're looking at the phone screen in a poorly lit room or in the dark.