The good news is that salt dissolves readily in water, which is cheap and easy to find.
According to Lynn Krafft, ICAN/ATEX editor, the best way to handle your mats is to hang them over racks and hose them down until the water runs clean. You can either wet vacuum or let them drip dry.
Carpets will need hot water rinse extraction. Use enough rinse and vacuum passes to dissolve the salt and remove the residue. Be careful not to over-wet the carpet, especially if it an economic grade, as over-saturation can erode the backing material. Concentrate on the entry areas and the traffic lanes.
The use of an acid rinse agent in the rinse tank may be a good way to leave the carpets on the neutral side and facilitate the rinsing.