I think I agree that Alters can't be killed. For whatever reason, your brain has created a range of versions of yourself that are designed to cope with situations that seem threatening. But the threat doesn't have to be logical (it can simply be from a seemingly benign trigger - I have an aggressive alter that comes out when I walk on particular coloured carpet), and the way that Alter behaves and 'copes' is very often problematic.
I've definitely found that I can reduce the problems that certain Alters create if I can reach out to that part of myself & work with it (easier said than done) to essentially re-teach that part of my mind about safety and acceptable behaviour. As much as I loathe some of my Alters, they are all parts of who I am, and even though they can be destructive and difficult to understand, they have been created (by you) to protect you. They'll keep doing their job the only way they know how until you can teach them how to work as part of the team. The question for me isn't "can I kill it?", but rather, "why did my brain think that creating that Alter was necessary, and how do I get it to grow up and play ball with the rest of us"?
I don't think I've met anyone with DID who likes all of their Alters. But they're part of you, they each bring their own strengths to protect you, and in their own messy way, protecting you is actually the only reason they exist.
If it were me, now I knew that Alter existed, I'd hunt it down, try and get to know it, and work on helping in cooperate with the rest of the team. I don't think you get to drop players from your team in DID, so we're stuck with trying to communicate, appreciate each other's efforts, and with some work, show them a better way to function.