I don't know of a Christian origin for the salt belief, but in many Afro-Craibbean religions, it is traditional and probably entered the Pagan belief system through Hoodoo in the Western World rather early during the slave trade/cultural blending among European superstitions and Afro superstitions. OR, it may have been added into Afro-Carib religions from the European folkloric system, like poppets did, but which Vodou gets blamed for to this day
The theory is that the spirits of the Dead are about decay and attracted to it, hence since salt preserves, it repels them. One sprinkles a pinch or so in every single corner of their home, including closets, and blesses the rest using Florida Water, or Holy Water, to cleanse a residence of negativity and bad spirits. Some add burning pleasant incenses better suited for cleansing lower level entities, such as Frankincense and/or myrrh or white sage, and some then close it up by blessing all windows and doorways with olive oil or Florida Water, often in the form of tiny crosses, while praying and asking for what they intend - in this case cleansing of all bad things and a request for God's blessing on the home and peace.
This is best done by a person who owns or is the authority figure of a household, like the father or mother, or else by an ordained priest in a religion which deals with this sort of thing. It is less effective done by outsiders inside someone else's home, unless they are ordained. Self initiates are not ordained in the sense I mean.
That is how it is viewed, generally speaking, in the Diasporic religions.
So, now you've gotten several straight answers

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YMMV
NS