© 2017 American Physical Society. We apply the first-order reversal curve (FORC) method, adapted from studies of ferromagnetic materials, to the magnetostructural phase transition of Fe1+yTe. FORC measurements reveal two features in the hysteretic phase transition, even in samples where traditional temperature measurements display only a single transition. For Fe1.13Te, the influence of magnetic field suggests that the main feature is primarily structural while a smaller, slightly higher-temperature transition is magnetic in origin. By contrast, Fe1.03Te has a single transition which shows a uniform response to magnetic field, indicating a stronger coupling of the magnetic and structural phase transitions. We also introduce uniaxial stress, which spreads the distribution width without changing the underlying energy barrier of the transformation. The work shows how FORC can help disentangle the roles of the magnetic and structural phase transitions in FeTe.