How can I hide an object line rendered in a minicam?

I have an animal moving in my scene. I have a line renderer attached to it to draw an oval around it so the animal appears larger and easier to click on. I have a minimap which shows a zoomed in view. Here the animal is large so I do not want to see the line around the animal. Is there a way to hide this component (the line renderer) of the object in the minimap? I am thinking of layers but that seems to apply to the whole object (animal). What I really need is a layer for a component of the object. Any suggestions? Thank you.

Add the line renderer as the child object, and set the later of the child object.