What type of material grips best on a laminate desk without leaving permanent residue?

Natural rubber is the winner. It sticks to smooth surfaces like laminate just enough to hold firm but doesn’t form a permanent bond. Silicone can slide around on a dusty or warm desk, and foam mats may compress, peel, or leave sticky residue. Look for a flat, non-textured natural rubber mat—the kind used in kitchen drawer liners works great and is cheap.