Hi chemist

Those exposed roots can be watered whenever you water the other roots. I would not cover them with a wet paper towel. You can spray (mist) those roots occasionally if you like (but try to avoid wetting the leaves).

Remember that the roots of epiphytic orchids are designed to be exposed to air (growing on trees in nature, orchid roots are exposed to air every day). Most of the thickness of an orchid root is a tissue called velamen that stores moisture around the true root (the root is inside the layer of velamen). So, unlike the root of an African violet, or a bean plant, etc., it is OK if the Phal roots are dry occasionally.