The mass of the object on Neptune is equal to its mass on Earth.
In fact, the mass is an intrinsic property of an object, so it does not depend on external conditions. The weight of the object, instead, depends on the gravity of the planet, according to:
where m is the mass of the object and g is the strength of the gravitational field of that planet. In this case, since the gravity on Neptune is 1.1 times the gravity on Earth, g on Neptune is 1.1 times g on Earth, so the weight on Neptune will be 1.1 times the weight on Earth.