Not at all. Whatever works best. I threw that together quickly.
I've done work on Visual Pinball tables and have had the same issue. I would try a variety of settings in Photoshop but then when I imported it into the game, it would define whatever edges it felt like. Probably some of the built-in anti-aliasing. I would have to find workarounds like you did here. If you haven't tried "nearest neighbor" as the image interpolation in Photoshop, give that a try.
I finally found a picture showing how that mountain backdrop worked. All the pictures show it in some kind of plastic sleeve. I just assumed that it was packaged this way. It actually has an opening that allows it to slide over the entire game.
You mentioned that Super Mario had one? I've never actually seen a picture of one for that game or Climber.
View my gameplay videos:
Light Gun Games with Aimtrak
Trackball Games with X-Arcade Trackball
Star Wars Episode 1 Racer with Dual Throttle Controls