  We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D
torus $\mathbb{T}^2$, perturbed by multiplicative transport noise. The equation
admits the white noise measure on $\mathbb{T}^2$ as the invariant measure. We
first prove the existence of white noise solutions to the stochastic equation
via the method of point vortex approximation, then, under a suitable scaling
limit of the noise, we show that the solutions converge weakly to the unique
stationary solution of the dissipative mSQG equation driven by space-time white
noise. The weak uniqueness of the latter equation is also proved by following
Gubinelli and Perkowski's approach in \cite{GP-18}.
