Optical nanoantennas have attracted a lot of research interest over the last decade owing to their unique characteristics in concentrating far-field radiation into the sub-wavelength dimensions. Also, they have been recently utilized to enhance the functionality of nonlinear optical devices. By inserting a dielectric nanoparticle within the gap of a dipole nanoantenna, the third-harmonic generation (THG) emission can be boosted. In this study, we simulate dipole and bowtie nanoantennas and compare their THG output spectra with and without the presence of indium tin oxide (ITO) nanocrystal in the nanoantennas gap. The results show that with proper design of the nanoantenna and changing the geometry from the dipole to the bowtie shape as well as inserting the ITO nanocrystal, the THG efficiency can be enhanced by a factor of three, which is higher than the dipole counterpart reported in recent established works. Our work opens a new window to generate more efficient nonlinear phenomena at nanoscale devices.