Linen: no need for particular care, should you get marks then gently buff with a clean damp cloth. Should you have stubborn marks you may try to use a qualiy stain remove for delicate fabrics but please test in a corner first. Nubuck: no need for any particular care
After any use always allow the Lune Slippers to dry at room temperature, away from any direct heat source. If your Sagans have got wet you may roll-up some paper and insert it inside the Lune slippers.