Those do not do what you are thinking they do....I would effort towards fixing or replacing. You're not going to like it if you remove it or it comes off the rest of the way. After hitting bumps, potholes, etc. for a while, the bottom of the spring will shift and the inner porting of the spring that sits on the lower spring mount will contact metal-on-metal. Eventually, all of the squeaking will sound like a flock of little birds is going everywhere you are. It also prevents long term wear of the spring and mount.
Also, you can spray some adhesive like 3M 77 on the inside of the spring sleeves to help them stick to the coil.
Friend's Max Tow we just lifted had coil pads under springs on both ends, and the isolators on top. Cannot say what mine has/had, as my wife had the rubicon suspension added while I was at work... will be lifting sometime between fall/spring.@Artsifrtsi,
There are no isolator pads on the rear bottom coils, at least on a '21 Mojave (I suppose different models and year could be different). It is just a coil sleeve between the coil and the lower mount, and the sleeve you are referring to towards the top of the spring. I'm not sure there is any dampening in the thin upper coil sleeve, but it does keep the upper portion of the coil from making noise. You can see the lower sleeve it in the picture posted by the OP, and in these snips of a stock coil:
It was such when I did my lift install. Here's mine right now after forgetting to install the lower spring sleeves...
And it does squeak without the sleeve in this metal-to-metal contact.