Saline nasal irrigation delivers chloride ions to nasal epithelial cells, which increases their production of hypochlorous acid to fight viral infections.

Study: Hypertonic saline nasal irrigation and gargling should be considered as a treatment option for COVID-19

The study shows that using saltwater nose rinses helps your nose cells make a natural virus-fighting chemical, just like the claim says.

Study: A pilot, open labelled, randomised controlled trial of hypertonic saline nasal irrigation and gargling for the common cold

The study used saltwater nose rinses like the claim describes and found it helped people get better faster from colds, which supports the idea that it fights viruses, but it didn't check the exact chemical process mentioned.

Study: Antiviral innate immune response in non-myeloid cells is augmented by chloride ions via an increase in intracellular hypochlorous acid levels

The study shows that adding salt (sodium chloride) helps cells make more bleach-like acid to fight viruses, which matches the claim about saltwater nose rinses doing the same thing.