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When selecting a rigid body in Motive 1.5.1, there is an option to "reset to current orientation".
How is the new orientation computed? Does the inverse quaternion of the current orientation get multiplied from the left hand side?

When Reset to current orientation is computed, it reorients the rigid body markers, so that the rigid body, based on it's current pivot point and orientation so that the rigid body reports 0,0,0,1 for quaternion orientation, and 0 for yaw, pitch, and roll. Position results remain unchanged. It's calculated a bit differently than what you describe but delivers the same result.