We investigated the gate control of a two-dimensional electron gas (2DEG) confined to InSb quantum wells with an Al2O3 gate dielectric formed by atomic layer deposition on a surface layer of Al0.1In0.9Sb or InSb. The wider bandgap of Al0.1In0.9Sb compared to InSb resulted in a linear, sharp, and non-hysteretic response of the 2DEG density to gate bias in the structure with an Al0.1In0.9Sb surface layer. In contrast, a nonlinear, slow, and hysteretic (nonvolatile-memory-like) response was observed in the structure with an InSb surface layer. The 2DEG with the Al0.1In0.9Sb surface layer was completely depleted by application of a small gate voltage (-0.9 V).