The scale mapping solution only works if you don't have to look around with your camera, otherwise you will notice the sphere-like background image has been stretched.

A correct way to do this scale is actually changing the Field Of View (or Focal Length in blender) of your camera, for this:

 1. Select your camera
 2. In the 3D Viewport: <kbd>Right Mouse Click</kbd> > *Camera Lens Angle* and drag

or

- In the *Properties* panel click the green camera tab, in *Lens* section change the *Focal Length* field