Apple doesn't recommend, nor not recommend camera lens protectors. But they do add another layer light has to pass through, so I DON'T recommend them. The lenses covering the camera on your iPhone are Sapphire, so very hard to scratch (though sapphire can be shattered). That said, the light appearing above the mood is called lens flare and very common when photographing something bright like the sun or moon. You could actually see the flare in the photo before you took it (though you likely didn't notice it) and had you angled the phone differently, you would have seen the flare diminish or go away. It's all in how the light hits the sensor on your camera.
Here are two photos I took to illustrate lens flare and how to eliminate them by angling the phone different to the lights:
Photo with Lens flare at night (see the green dots above the lights on my deck)

Now, simply by angling the camera differently (I never moved my location, just the angle of the camera), the flares are completely gone:

Lens flare is a normally occurring feature of digital photography. With patience and time in composition, you can avoid or eliminate it, but not always, like when photographing really bright lights (such as moon or sun).