What to do about the rubber gasket between the bezel and monitor?

The gasket has two functions to hold the display away from the keyboard just enough so the keys don’t rub the glass which over time burnishes marks into the displays coatings. The second is to prevent debris and wet into the area that can splash up when the display is down (still limited protection).

Once the rubber has split it often won’t stay put. Apple over the years has reduced the serviceable parts count and sadly Apple only lists the full display as a replaceable part in this series. Even still see if our buddies at TheBookYard can help you as they do parts recovery from dead systems.