We consider the characteristics of THz antenna made of circular layered dielectric rod, which mimics the Luneburg lens, decorated with conformal microsize graphene strip. The strip has arbitrary angular size and location and its surface impedance is characterized with the quantum Kubo theory. We build mathematically accurate algorithm, which uses the method of analytical regularization (MAR) based on explicit inversion of the static part of the problem, that has mathematically guaranteed convergence. We study the frequency dependences of the total scattering and absorption cross-sections of this scatterer in wide range from zero to 10 THz. This analysis supports the presence of the broadband electromagnetic-jet effect of lens-like dielectric rod and the resonances on the moderate-Q plasmon modes of graphene strip.