Using polarized and unpolarized neutron scattering we show that interstitial Fe in superconducting Fe_{1+y}Te_{1-x}Se_x induces a magnetic Friedel-like oscillation that diffracts at Q_(in-plane)=(1/2,0) and involves >50 neighboring Fe sites. The interstitial >2 mu_B moment is surrounded by compensating ferromagnetic four spin clusters that may seed double stripe ordering in Fe_{1+y}Te. A semi-metallic 5-band model with (1/2,1/2) Fermi surface nesting and four fold symmetric super-exchange between interstitial Fe and two in-plane nearest neighbors largely accounts for the observed diffraction.
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