What does remux mean in movies?

Remux means the data has been copied (often simply to a new container like mkv) without any changes. So a BluRay release without the ‘remux’ tag means that the media has been reencoded and there is loss of quality, while ‘remux’ means it is lossless.

What is remux 4K?

The remux will be the exact full quality you’d get from the actual 4K Blu Ray disk, the encode is well, encoded. The process of encoding makes files smaller by comprising on video quality and audio tracks (most of the time) but depending on the encode, you may or may not be able to tell the difference between the two.