[2020] So I have this objective that leads to nothing? And it won't go away. If I set my objective to something else, like a quest, sometimes it won't show the quest objective, and most of the time, it will make this one go away, but it just comes back.

Your activity tracker has 5 slots, so can consequently track a path and a quest at the same time.

You presumably have an objective from one of the Lumbridge skilling paths in your activity tracker.

You can right-click an activity in your activity tracker and choose Remove to remove it.

(Given the destination, the achievement's probably called You Doity Rat, It Was Dead Already, Camping Trip, or Ratatouille - Lumbridge path cooking rat meat.)

If your activity tracker isn't on your screen (assuming you're playing with the new interface system on the Desktop client), hover the sword and shield on your ribbon and press the Activity Tracker icon (looks like a pirate's treasure map).