  We revisit the 3d GLSM computation of the equivariant quantum K-theory ring
of the complex Grassmannian from the perspective of line defects. The 3d GLSM
onto $X={\rm Gr}(N_c, n_f)$ is a circle compactification of the 3d
$\mathcal{N}=2$ supersymmetric gauge theory with gauge group $U(N_c)_{k, k+l
N_c}$ and $n_f$ fundamental chiral multiplets, for any choice of the
Chern-Simons levels $(k,l)$ in the `geometric window'. For
$k=N_c-\frac{n_f}{2}$ and $l=-1$, the twisted chiral ring generated by the
half-BPS lines wrapping the circle has been previously identified with the
quantum K-theory ring QK$_T(X)$. We identify new half-BPS line defects in the
UV gauge theory, dubbed Grothendieck lines, which flow to the structure sheaves
of the (equivariant) Schubert varieties of $X$. They are defined by coupling
$\mathcal{N}=2$ supersymmetric gauged quantum mechanics of quiver type to the
3d GLSM. We explicitly show that the 1d Witten index of the defect worldline
reproduces the Chern characters for the Schubert classes, which are written in
terms of double Grothendieck polynomials. This gives us a physical realisation
of the Schubert-class basis for QK$_T(X)$. We then use 3d $A$-model techniques
to explicitly compute QK$_T(X)$ as well as other K-theoretic enumerative
invariants such as the topological metric. We also consider the 2d/0d limit of
our 3d/1d construction, which gives us local defects in the 2d GLSM, the
Schubert defects, that realise equivariant quantum cohomology classes.
