Traditionally (pre-ai) you would use another image of the same part of the sky and negate the items that you want to remove from the image
As an example terrestrial telescope mirrors get dusty. You're not going to break down the scope just to clean up the dust as this is a many days operation in most cases. So instead you would take "flats" that were of a pure white background and thus showed the dust in its full, dusty, glory. When you take your actual images, you negate (subtract from the original image) the flat and thus any noise generated by the dust. You can use this same method for removing brighter stars from an image that would otherwise saturate the ccd and wash out the background. Turns out it doesn't work for planes. Ask me how I know!
Why does the technique not work with aircraft? Because they generally fly on fixed routes?
Earth moves - that's how you get the next shot without repositioning the telescope.
This time-lapse probably better visualizes it: https://www.youtube.com/watch?v=wFpeM3fxJoQ
As the Earth rotates over the course of the night, the background stars and nebulae move as a single unit, no?
Maybe for some close stars parallax might work to remove them over the course of half a year. But no way could the Earth's rotation during a single night move background stars out of a nebulae.
Sure, but the nebulae also move along with the stars. The questions is how one can subtract the stars without also subtracting the nebulae. (I'm assuming different filters and/or a database of known star positions)
The ESA catalog is not precise enough to remove a star from an image of the structure of a nebulae - never mind Hipparcos. Filters while photographing and image processing in post are the way to go.
Don't forget that not only does the star need to be removed, but also the diffraction spikes. Those are internal reflections in the lens assembly - not mapped by any star catalog ))
Makes sense, thanks!