Interactions between microorganisms and solid boundaries play an important role in biological processes, such as egg fertilization, biofilm formation, and soil colonization, where microswimmers move within a structured environment. Despite recent efforts to understand their origin, it is not clear whether these interactions can be understood as being fundamentally of hydrodynamic origin or hinging on the swimmer's direct contact with the obstacle. Using a combination of experiments and simulations, here we study in detail the interaction of the biflagellate green alga Chlamydomonas reinhardtii, widely used as a model puller microorganism, with convex obstacles, a geometry ideally suited to highlight the different roles of steric and hydrodynamic effects. Our results reveal that both kinds of forces are crucial for the correct description of the interaction of this class of flagellated microorganisms with boundaries.