  Fe$_{1+x}$Te is a two dimensional van der Waals antiferromagnet that becomes
superconducting on anion substitution on the Te site. The parent phase of
Fe$_{1+x}$Te is sensitive to the amount of interstitial iron situated between
the iron-tellurium layers displaying collinear magnetic order coexisting with
low temperature metallic resistivity for small concentrations of interstitial
iron $x$ and helical magnetic order for large values of $x$. While this phase
diagram has been established through scattering [see for example E. E.
Rodriguez $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 064403 (2011) and S.
R\"ossler $\textit{et al.}$ Phys. Rev. B ${\bf{84}}$, 174506 (2011)], recent
scanning tunnelling microscopy measurements [C. Trainer $\textit{et al.}$ Sci.
Adv. ${\bf{5}}$, eaav3478 (2019)] have observed a different magnetic structure
for small interstitial iron concentrations $x$ with a significant canting of
the magnetic moments along the crystallographic $c$ axis of $\theta$=28 $\pm$
3$^{\circ}$. In this paper, we revisit the magnetic structure of Fe$_{1.09}$Te
using spherical neutron polarimetry and scanning tunnelling microscopy to
search for this canting in the bulk phase and compare surface and bulk
magnetism. The results show that the bulk magnetic structure of Fe$_{1.09}$Te
is consistent with collinear in-plane order ($\theta=0$ with an error of $\sim$
5$^{\circ}$). Comparison with scanning tunnelling microscopy on a series of
Fe$_{1+x}$Te samples reveals that the surface exhibits a magnetic surface
reconstruction with a canting angle of the spins of $\theta=29.8^{\circ}$. We
suggest that this is a consequence of structural relaxation of the surface
layer resulting in an out-of-plane magnetocrystalline anisotropy. The magnetism
in Fe$_{1+x}$Te displays different properties at the surface when the symmetry
constraints of the bulk are removed.
