  In this paper, we give a combinatorial description of the concordance
invariant $\varepsilon$ defined by Hom in \cite{hom2011knot}, prove some
properties of this invariant using grid homology techniques. We also compute
$\varepsilon$ of $(p,q)$ torus knots and prove that
$\varepsilon(\mathbb{G}_+)=1$ if $\mathbb{G}_+$ is a grid diagram for a
positive braid. Furthermore, we show how $\varepsilon$ behaves under
$(p,q)$-cabling of negative torus knots.
