Amplifying local electromagnetic fields by engineering optical interactions between individual constituents of an optical antenna is considered fundamental for efficient nonlinear wavelength conversion in nanometer-scale devices. In contrast to this general statement we show that high field enhancement does not necessarily lead to an optimized nonlinear activity. In particular, we demonstrate that second-harmonic responses generated at strongly interacting optical gap antennas can be significantly suppressed. Numerical simulations are confirming silencing of second-harmonic in these coupled systems despite the existence of local field amplification. We then propose a simple approach to restore and amplify the second-harmonic signal by changing the manner in which electrically-connected optical antennas are interacting in the charge-transfer plasmon regime. Our observations provide critical design rules for realizing optimal structures that are essential for a broad variety of nonlinear surface-enhanced characterizations and for realizing the next generation of electrically-driven optical antennas.