  A promising way to measure the distribution of matter on small scales (k ~ 10
hMpc^-1) is to use gravitational lensing of the Cosmic Microwave Background
(CMB). CMB-HD, a proposed high-resolution, low-noise millimeter survey over
half the sky, can measure the CMB lensing auto spectrum on such small scales
enabling measurements that can distinguish between a cold dark matter (CDM)
model and alternative models designed to solve problems with CDM on small
scales. However, extragalactic foregrounds can bias the CMB lensing auto
spectrum if left untreated. We present a foreground mitigation strategy that
provides a path to reduce the bias from two of the most dominant foregrounds,
the thermal Sunyaev-Zel'dovich effect (tSZ) and the Cosmic Infrared Background
(CIB). Given the level of realism included in our analysis, we find that the
tSZ alone and the CIB alone bias the lensing auto spectrum by 0.6 sigma and 1.1
sigma respectively, in the lensing multipole range of L in [5000,20000] for a
CMB-HD survey; combined these foregrounds yield a bias of only 1.3 sigma.
Including these foregrounds, we also find that a CMB-HD survey can distinguish
between a CDM model and a 10^-22 eV FDM model at the 5 sigma level. These
results provide an important step in demonstrating that foreground
contamination can be sufficiently reduced to enable a robust measurement of the
small-scale matter power spectrum with CMB-HD.
