Well...yes and no. Depends on what you mean by the intensity of the gravitational pull of the earth. The Earth exerts a larger gravitational force on more massive objects (objects fall with the same acceleration because mass has the peculiar property of creating gravitational force, and resisting it as well). So in that sense, the "intensity" of the Earth's gravitational pull is zero when it has nothing to draw upon, and the intensity increases proportionately with the mass of the object that it is pulling. If by "intensity" you mean force, then yes, the intensity of the gravitational pull of the Earth certainly does depend on the presence of an object, and the intensity is zero when there's no object present.
However, physicists have invented the concept of the gravitational field, whereby we obscure any mass that the Earth might be pulling on, and talk about the force per unit mass that the Earth would exert on a hypothetical point mass. The gravitational field is not dependent on the existence of any other mass, and indeed we believe that the gravitational field is there even when it has nothing to pull on. If this is what you mean by intensity, then no, intensity doesn't depend on the existence of any object for the Earth to draw upon.