What is this strange looking piece of plastic doing on my telescope?
Telescope companies began shipping telescopes with a red dot finder, a cheap piece of plastic that projects a red dot onto a small piece of viewing plastic. Using the human eye, objects visible can be found and centered. This is usually the Moon and brighter stars. For areas of heavy light pollution, it won't show any stars dimmer than what the human eye can see, so basic star hopping may not be an option. The illustration shows the Orion EZ Finder II for $39.99 and it's included on beginner telescopes. The same red dot finder sells for about $12 from China sources. The device uses a button battery and it's easy to forget and leave the finder on and then the battery burns out and needs replacing. Button batteries are not always easy to find at the store.
The finder design is not new. Many old timers will remember the Telrad finder from decades ago. It originated in the late 1970s when Steve Kufeld of Huntington Beach, California came up with the idea to manufacture an economical sight to help amateur and professional astronomers find their way across the night sky. "The Telrad is a different kind of device for aiming a telescope. It has been very popular with amateur astronomers since its introduction in 1978. The Telrad works on an entirely different principle, and has some distinct advantages over its optical finder scope cousin.
Using a lens and light from a red LED and a glass beam splitter, the Telrad projects a nearly parallax-free, illuminated red bulls-eye into the observer’s eye. When the observer looks through the glass window, the bulls-eye appears to be projected onto the sky." Source
While the red dot finder is a great invention, and good for bright objects and beginners, the telescope may need another finder for dim objects. I recommend a 5x24 finderscope with lenses to see dimmer stars over the human eye, but not too many stars making the star field confusing. A 6x50 finderscope might show too many stars. It depends on the location and application. One could keep the red dot finder for locating bright objects and add another finder to the telescope for seeing dimmer stars when starhoping.
More about red dot finders, etc.
Orion Starblast Telescopes have a red dot finder
Celestron FirstScope 5x24 Finderscope