  Let $\mathcal G\subset L^2(\mathbb R)$ be the subspace spanned by a Gabor
Riesz sequence $(g,\Lambda)$ with $g\in L^2(\mathbb R)$ and a lattice
$\Lambda\subset\mathbb R^2$ of rational density. It was shown recently that if
$g$ is well-localized both in time and frequency, then $\mathcal G$ cannot
contain any time-frequency shift $\pi(z) g$ of $g$ with $z\notin\Lambda$. In
this paper, we improve the result to the quantitative statement that the
$L^2$-distance of $\pi(z)g$ to the space $\mathcal G$ is equivalent to the
Euclidean distance of $z$ to the lattice $\Lambda$, in the sense that the ratio
between those two distances is uniformly bounded above and below by positive
constants. On the way, we prove several results of independent interest, one of
them being closely related to the so-called weak Balian-Low theorem for
subspaces.
