We consider star-like polymers with weak, that is, pH-dependent, hydrophobic polyelectrolyte arms. For low ionic strength conditions, a microphase-segregated quasimicellar structure is found, for which the star features a compact apolar core and a charged and swollen corona. This state is jump-like lost when the ionic strength is increased, i.e., at some intermediate ionic strength value. Using numerical self-consistent field modeling, we focus on the adsorption characteristics of these objects onto hydrophobic surfaces as a function of the ionic strength. In the quasimicellar state, the stars are attracted to the surface, albeit that, typically, an adsorption barrier is present. The strongest repulsion is found at intermediate ionic strength, where the star-like molecule is in a single-phase state and the barrier remains modest at both low and high ionic strength cases. Remarkably, it is possible that a star in a single swollen phase state is pushed into the quasimicellar state.