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:
- Select your camera
- In the 3D Viewport: Right Mouse Click > Camera Lens Angle and drag
or
- In the Properties panel click the green camera tab Lens section change the Focal Length field
