The inelastic response of a Borromean trimer composed of three identical bosons is explored. To this end we use the quadrupole approximation as the excitation mechanism of the bosonic system from its ground state. We utilize the hyperspherical-harmonics expansion to solve the Schroedinger equation and the Lorentz integral transform method to calculate the reaction. It is found that the magnitude of the response function and corresponding sum rules increase as a power law when approaching the three-body threshold. It is also found that this increase is governed by unnatural exponents.