The glass screen on the iPhone is designed to be scratch-resistant, but that doesn't mean that the screen won't occasionally get scratched anyway. If your iPhone screen has been scratched, that doesn't mean the defect has to be there forever. You can remove the scratch on your iPhone with a few different commercial products, or even a tube of regular toothpaste.
Purchase either iDrops, Brasso or a tube of toothpaste. If you choose the toothpaste option, opt for the most basic type of toothpaste you can find. Avoid whitening toothpastes and those with crystals or baking soda in them, as they will be more abrasive than a basic, traditional paste.
Apply a small amount of the polish or paste of your choice onto your soft cloth and begin rubbing it gently into the screen. Your goal is to essentially rub the scratch out, so the length of time you need to polish your screen will depend on how deep your scratch is.
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Moisten another area of the cloth with water and gently wipe the screen to remove any excess polish. Avoid getting areas such as the speakers and buttons wet, as moisture can cause damage to your phone should it get inside.
Repeat the process as needed to further remove the scratch. Deep scratches can require a great deal of polishing, and may be best removed in several shorter sessions.