fitting
The compression ring crushes into the line when applied properly, making it nearly impossible to get the ring off without damaging the line. Otherwise your compression fitting would leak between the line and ring. Even if you do manage to get the old ring off, if you put a new ring in the spot where the old one was, it still may not seal well. You really have two options, use the old ring and nut if in good shape and see if they leak (this has worked for me on a number of occasions). Alternately you can cut the line just underneath the ring and use a new nut and ring.