We present the first study of an Iwasawa-Taniguchi/'X-ray Baldwin' effect for Compton-thick active galactic nuclei (AGN). We report a statistically significant anticorrelation between the rest-frame equivalent width (EW) of the narrowcore of the neutral FeK alpha fluorescence emission line, ubiquitously observed in the reflection spectra of obscured AGN, and the mid-infrared 12 mu m continuum luminosity (taken as a proxy for the bolometric AGN luminosity). Our sample consists of 72 Compton-thick AGN selected from pointed and deep-field observations covering a redshift range of z similar to 0.0014-3.7. We employ a Monte Carlo-based fitting method, which returns a Spearman's Rank correlation coefficient of rho= -0.28 +/- 0.12, significant to 98.7 per cent confidence. The best-fitting found is log(EWFeK alpha) alpha -0.08 +/- 0.04 log(L-12 mu m), which is consistent with multiple studies of theX-ray Baldwin effect for unobscured and mildly obscured AGN. This is an unexpected result, as the FeK alpha line is conventionally thought to originate from the same region as the underlying reflection continuum, which together constitute the reflection spectrum. We discuss the implications this could have if confirmed on larger samples, including a systematic underestimation of the line-of-sight X-ray obscuring column density and hence the intrinsic luminosities and growth rates for the most luminous AGN.