In the US there is ample legal president that this is legal.
Digitizing a photo or painting that is in the public domain should not create a new copyright on that copy, because an original work was not created. Bridgeman Art Library v. Corel Corp establishes a precedent that “Even though accurate reproductions might require a great deal of skill, experience and effort, the key element to determine whether a work is copyrightable under US law is originality.”
In other parts of the world this is less settled, but in the UK the National Portrait Gallery threatened Wikipedia for hosting their scans of old paintings. The museum backed down and the UK’s Intellectual Property Office then later said that “copyright can only subsist in subject matter that is original in the sense that it is the author’s own ‘intellectual creation’. Given this criteria, it seems unlikely that what is merely a retouched, digitized image of an older work can be considered as ‘original’.”
So in the US and probably the UK you should be fine to freely use and modify restorations as long as the original film is public domain.
Now, a lot of restoration houses do put copyright notifications on their work. They do this mostly so they can get paid for when another label wants to use their transfer. Because their business model depends on this it’s conceivable that they might go to court to try and defend them. You would probably win if you could afford to hire a lawyer and defend your case, but you couldn’t then this would be an effective way to stop usage of their transfer.
There are weird areas this gets into such as if the restored tinting on silent films is copyrightable because it’s a creative decision, or because since the tinting aims to restore an original element of the film it is not copyrightable. Also, based on how the music industry works, multi-channel remixed soundtracks (from the original elements) are likely copyrightable depending on the creative decisions made.
Edit: And just beaten to it by Mr Shickadance
Nah, not beaten. Very interesting stuff.