  We study the GIT quotient of the minimal Schubert variety in the Grassmannian
admitting semistable points for the action of maximal torus $T$, with respect
to the $T$-linearized line bundle ${\cal L}(n \omega_r)$ and show that this is
smooth when $gcd(r,n)=1$. When $n=7$ and $r=3$ we study the GIT quotients of
all Richardson varieties in the minimal Schubert variety. This builds on
previous work by Kumar \cite{kumar2008descent}, Kannan and Sardar
\cite{kannan2009torusA}, Kannan and Pattanayak \cite{kannan2009torusB}, and
recent work of Kannan et al \cite{kannan2018torus}. It is known that the GIT
quotient of $G_{2,n}$ is projectively normal. We give a different combinatorial
proof.
