First it’s possible to send up a camera that would be sensitive enough to use starlight to capture images on the dark side. However, those things aren’t light and would come at the cost of less propellant for minimal gain. Adding a tiny camera and a tiny light at the same time would also be possible but there really isn’t anything worth looking at via a single camera.

As to using infra red camera, they simply don’t work on objects the same temperature as the camera. NASA could have sent one up with a cooling system to look at the cold side of the sunshade, but again weight and pointlessness means it’s just wasteful.