The rubber gasket around my Macbook screen is coming off!
Okay, first things first. It's definitely worth you taking it in to an Apple Store (if you're able to) or phoning Apple support about this. I have known Apple to replace this even if you're technically outside their warranty period. Of course, each case is different, and it will depend on the What, When, How and Why of your situation. In a nutshell, it doesn't hurt to ask.

Now, regarding whether this has to involve the replacement of your entire screen, the answer is not so straightforward.

Officially Apple does not supply the rubber as a separate part, instead it comes with a new lid/screen replacement. However, I have known Apple to replace the rubber on its own, so they can do it.

Also, I'm personally aware of this being done by following the same steps of replacing the screen - except that you only go as far as removing the old gasket and then follow the steps in reverse to add the new gasket and put everything back together again.

If you have no joy at Apple you can choose to repair it yourself (if it's not something that scares you).

To repair it yourself you can purchase a new gasket from places like eBay. Of course the steps involved can be found online or you could ask another question here for guidance.