A profound understanding of the properties of unmodified and saturated fatty acid-modified calcite surfaces is essential for elucidating their resistance and stability in the presence of water droplets. Additional insights can be obtained by also studying the effects of carboxylic acid-saturated aqueous solutions. We elucidate surface wettability, structure, and nanomechanical properties beneath and at the edge of a deposited droplet after its evaporation. When calcite was coated by a highly packed monolayer of stearic acid, a hydrophilic region was found at the three-phase contact line. In atomic force microscopy mapping, this region is characterized by low adhesion and a topographical hillock. The surface that previously was covered by the droplet demonstrated a patchy structure of about 6 nm height, implying stearic acid reorganization into a patchy bilayer-like structure. Our data suggest that during droplet reverse dispensing and droplet evaporation, pinning of the three-phase contact line leads to the transport of dissolved fatty carboxylic acid and possibly calcium bicarbonate Ca(HCO3)2 molecules to the contact line boundary. Compared to the surface of intrinsically hydrophobic materials, such as polystyrene, the changes in contact angle and base diameter during droplet evaporation on stearic acid-modified calcite are strikingly different. This difference is due to stearic acid reorganization on the surface and transport to the water-air interface of the droplet. An effect of the evaporating droplet is also observed on unmodified calcite due to dissolution and recrystallization of the calcite surface in the presence of water. In the case where a water droplet saturated with octanoic acid is used instead of water, the stearic acid-coated calcite remains considerably more stable. Our findings are discussed in terms of the coffee-ring effect.