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A near pristine atomic cooling halo close to a star forming galaxy offers anatural pathway for forming massive direct collapse black hole (DCBH) seedswhich could be the progenitors of the $z>6$ redshift quasars. The closeproximity of the haloes enables a sufficient Lyman-Werner flux to effectivelydissociate H$_2$ in the core of the atomic cooling halo. A mild background mayalso be required to delay star formation in the atomic cooling halo, oftenattributed to distant background galaxies. In this letter we investigate theimpact of metal enrichment from both the background galaxies and the close starforming galaxy under extremely unfavourable conditions such as instantaneousmetal mixing. We find that within the time window of DCBH formation, the levelof enrichment never exceeds the critical threshold (Z$_{cr} \sim 1 \times10^{-5} \ \rm Z_{\odot})$, and attains a maximum metallicity of Z $\sim 2\times 10^{-6} \ \rm Z_{\odot}$. As the system evolves, the metallicityeventually exceeds the critical threshold, long after the DCBH has formed.

An analytic resolution to the competition between Lyman-Werner radiation and metal winds in direct collapse black hole hosts