Lipid membranes are key regulators of cellular function. An important step in membrane-related phenomena is the reshaping of the lipid bilayer, often induced by binding of macromolecules. Numerous experimental and simulation efforts have revealed that calcium, a ubiquitous cellular messenger, has a strong impact on the phase behavior, structural properties, and the stability of membranes. Yet, it is still unknown the way calcium and lipid interactions affect their macroscopic mechanical properties. In this work, we studied the interaction of calcium ions with membrane tethers pulled from giant unilamellar vesicles, to quantify the mechanical effect on the membrane. We found that calcium imposes a positive spontaneous curvature on negatively charged membranes, contrary to predictions we made based on the proposed atomic structure. Surprisingly, this effect vanishes in the presence of physiologically relevant concentrations of sodium chloride. Our work implies that calcium may be a trigger for membrane reshaping only at high concentrations, in a process that is robustly screened by sodium ions.