Analytical thin film peeling models, such as the Kendall model, are formulated under restricting assumptions concerning the strip geometry, the material behavior, the peeling kinematics, and the contact behavior. Recently, such models have been applied to study the peeling of gecko spatulae, although the gecko spatula is significantly different from an idealized thin film. The bending stiffness of the spatula especially has a strong influence on the peeling force which is neglected in the Kendall model. This is demonstrated here by several detailed finite element computations, based on a geometrically exact deformation model and a refined contact description for van der Waals adhesion. Therefore, the peeling of an elastic strip is considered and the influence of the bending stiffness is studied. It is shown that the adhesion induces a bending moment within the strip that can become very large and must, therefore, be accounted for in the strip formulation and evaluation of the work of adhesion. Further, the implications on the computation of the peeling behavior of gecko spatulae are discussed. It is observed that the spatula geometry lies in the range where the peeling work attains a maximum.