How do observational astronomers manage streaks and other artifacts from objects in Earth Orbit?
Simple - as you say, in order to get lots of dynamic range in deep astronomical images, you generally need to split your exposure time down into a number of sub-exposures.

When you combine these images, you don't just add them up, you "median stack" them (take the median on a pixel by pixel basis) or perform a slightly more sophisticated flux-weighted averaging that kicks out the outliers.

This process gets rid of any moving objects in the final image as well as cleaning up all the cosmic rays.

The problem with this reflector that has been launched is that it will be the equivalent of a very bright star. It will totally saturate any single image it appears in and might actually be bright enough to damage, or at least leave a persistent image, in some infrared detectors.