How can I know if North Atlantic Tracks have been amended?
For starters I am not completely knowledgeable with the North Atlantic Tracks but work with some of the other Flex track systems in the world. And they are all very similar.
The Track Messages are a type of NOTAM. They are released everyday and revised NOTAM (Track Message) is released if there are changes. They increment the alphabet character on the end of the TMI so that when a clearance is   issued by Air Traffic Control(ATC) they know which track they are flying including the version and ATC can correct it if the pilot has old information.
Extract from one of the Track Message:

REMARKS.

TMI IS 013 AND OPERATORS ARE REMINDED TO INCLUDE THE TMI NUMBER AS
PART OF THE OCEANIC CLEARANCE READ BACK.


When there is any changes they reissue the entire NOTAM (Track Message). So requesting accessing the message again will tell you straight away what is current. Usually aviation doesn't care about what it was, only what it is and what it will be. The computer systems that the airlines use get the most up to date data when they create the Flight Plans.
The question is what you want to do with the data to how the best way to get the data. But the link you supplied will always have the most recent ones.
Visualization of the these tracks, plus others, can be done on SkyVector. Go to layers to change any settings. The link automatically loads up on an ERC High with North American and Pacific Tracks Selected.