We consider the thermodynamic effects of an electrically charged impurity immersed in a two-dimensional two-component plasma, composed of particles with charges ±e, at temperature T, at coupling Γ = e2/(kBT) = 2, confined in a large disk of radius R. In particular, we focus on the analysis of the charge density, the correlation functions and the grand potential. Our analytical results show how the charges are redistributed in the circular geometry considered here. When we consider a positively charged impurity, the negative ions accumulate close to the impurity leaving an excess of positive charge that accumulates at the boundary of the disk. Due to the symmetry under charge exchange, the opposite effect takes place when we place a negative impurity. Both cases in which the impurity charge is an integer multiple of the particle charges in the plasma, ±e, and where a fraction of them are considered, require a slightly different mathematical treatment, showing the effect of the quantization of plasma charges. The bulk and the tension effects in the plasma described by the grand potential are not modified by the introduction of the charged particle. Apart from the effects due to the collapse coming from the attraction between oppositely charged ions, an additional topological term appears in the grand potential, proportional to -n2 ln(mR), with n the dimensionless charge of the particle. This term modifies the central charge of the system, from c = 1 to c = 1 - 6n2, when considered in the context of conformal field theories.