  We use scanning tunneling microscopy (STM) and quasiparticle interference
(QPI) imaging to investigate the low-energy orbital texture of single-layer
FeSe/SrTiO$_3$. We develop a $T$-matrix model of multi-orbital QPI to
disentangle scattering intensities from Fe $3d_{xz}$ and $3d_{yz}$ bands,
enabling the use of STM as a nanoscale detection tool of nematicity. By
sampling multiple spatial regions of a single-layer FeSe/SrTiO$_3$ film, we
quantitatively exclude static $xz/yz$ orbital ordering with domain size larger
than $\delta r^2$ = 20 nm $\times$ 20 nm, $xz/yz$ Fermi wave vector difference
larger than $\delta k$ = 0.014 $\pi$, and energy splitting larger than $\delta
E$ = 3.5 meV. The lack of detectable ordering pinned around defects places
qualitative constraints on models of fluctuating nematicity.
