  We examine the mid-infrared fluxes and spectral energy distributions for
metal-poor stars with iron abundances [Fe/H] $\lesssim-5$, as well as two
CEMP-no stars, to eliminate the possibility that their low metallicities are
related to the depletion of elements onto dust grains in the formation of a
debris disk. Six out of seven stars examined here show no mid-IR excess. These
non-detections rule out many types of circumstellar disks, e.g. a warm debris
disk ($T\!\le\!290$ K), or debris disks with inner radii $\le1$ AU, such as
those associated with the chemically peculiar post-AGB spectroscopic binaries
and RV Tau variables. However, we cannot rule out cooler debris disks, nor
those with lower flux ratios to their host stars due to, e.g. a smaller disk
mass, a larger inner disk radius, an absence of small grains, or even a
multicomponent structure, as often found with the chemically peculiar Lambda
Bootis stars. The only exception is HE0107-5240, for which a small mid-IR
excess near 10 microns is detected at the 2-$\sigma$ level; if the excess is
real and associated with this star, it may indicate the presence of (recent)
dust-gas winnowing or a binary system.
