Why must one use distilled water and not tap water? Will tap water with the salt packet damage the nose?

Tap water will not damage the nose, but there is a risk for contamination. All tap water is of different quality throughout the world and is not necessarily safe to enter the nasal passages. Water that is safe for drinking is not necessarily safe in the nasal passages and sinuses. This is why it is very important to use previously boiled and cooled water, distilled water, or commercially bottle water (in the USA) because it has gone through a proper filtration process.