Earlier quoted context omitted.
Now, don't take this as legal advice, but if the company re-scans/makes alterations to the image for display on the web, I think that counts as a new work But I'm a bit hazy about how derivative works are actually defined.
In the US context, it seems likely that the ruling in Bridgeman Art Library v. Corel Corp would preclude any copyright in such cases.
For instance, say a film's master negative has been affected by patches of mold and detail lost. As the original information has been actually lost at these points, any reconstruction 'originates' with the reconstruction 'artist'. In some instances the reconstruction involves no art as it's obvious what's missing—say an image of a quarter coin with a section missing out of it, whereas reconstructing the missing expression on a person's face may require interpretation and thus deemed new original art. Given the longstanding and heated debate over copyright, it seems to me these gray areas will be hotly contested.
Obviously, where new material is added there is no contest, new copyright is invoked. For example, some years back someone posted a medium resolution (720px) copy of Kino's rework of Buster Keaton's The General to the Internet Archive and it was eventually withdrawn.
I'm not conversant with any special copyright arrangements surrounding Keaton's works but presumably the takedown wasn't based on the cleaned up footage (given Bridgeman Art Library v. Corel Corp) but rather on the new soundtrack which accompanies the original silent footage.
Collaborative evidence of this is that other versions of The General weren't subject of the takedown. I vaguely recall that Keaton lost copyright over financial problems, if he'd been the copyright holder then we'd expect all copies to have been taken down (Keaton died in 1966 so if he'd still held the copyright at the time of his death then it would have been valid until 2056).