Tb2Ti2O7 is one of two compounds identified as potential quantum spin ices. As with other oxide pyrochlores the properties depend sensitively on the oxygen content. Most previous studies have aimed to work with samples as close to being stoichiometric as possible. Changes in the properties of Tb2Ti2O7 and Dy2Ti2O7 with oxygen-deficiency have recently been established. Here we propose to study the microscopic magnetic properties of oxygen-deficient Tb2Ti2O7 to compare with the extensive literature on stoichiometric samples.