Scene Capture 2D problems

I’m making a rifle scope using a scene capture component. I have created a render target that has the same size as the viewport. Then I created a material with that render target and assigned to the scope.

If I use default UVs, the whole scope content will get scaled; if I use TransformToClipSpace to calculate UVs, it will look fine. But the only problem is that, if I apply a camera shake, the scope content will never make a difference but the player camera does get changed, so it will look weird that the scope content is not synchronized. However, if I use default UVs, this problem will go away. So how to solve this?