  The repeating FRB 20190520B is localized to a galaxy at $z=0.241$, much
closer than expected given its dispersion measure $\rm DM=1205\pm4\ pc\
cm^{-3}$. Here we assess implications of the large DM and scattering observed
from FRB 20190520B for the host galaxy's plasma properties. A sample of 75
bursts detected with the Five-hundred-meter Aperture Spherical radio Telescope
shows scattering on two scales: a mean temporal delay $\tau(1.41\ {\rm
GHz})=10.9\pm1.5$ ms, which is attributed to the host galaxy, and a mean
scintillation bandwidth $\nu_{\rm d}(1.41\ {\rm GHz})=0.21\pm0.01$ MHz, which
is attributed to the Milky Way. Balmer line measurements for the host imply an
H$\alpha$ emission measure (galaxy frame) $\rm EM_s=620$ pc cm$^{-6} \times
(T/10^4 {\rm K})^{0.9}$, implying $\rm DM_{\rm H\alpha}$ of order the value
inferred from the FRB DM budget, $\rm DM_h=1121^{+89}_{-138}$ pc cm$^{-3}$ for
plasma temperatures greater than the typical value $10^4$ K. Combining $\tau$
and $\rm DM_h$ yields a nominal constraint on the scattering amplification from
the host galaxy $\tilde{F} G=1.5^{+0.8}_{-0.3}$ (pc$^2$ km)$^{-1/3}$, where
$\tilde{F}$ describes turbulent density fluctuations and $G$ represents the
geometric leverage to scattering that depends on the location of the scattering
material. For a two-screen scattering geometry where $\tau$ arises from the
host galaxy and $\Delta \nu_{\rm d}$ from the Milky Way, the implied distance
between the FRB source and dominant scattering material is $\lesssim100$ pc.
The host galaxy scattering and DM contributions support a novel technique for
estimating FRB redshifts using the $\tau-\rm DM$ relation, and are consistent
with previous findings that scattering of localized FRBs is largely dominated
by plasma within host galaxies and the Milky Way.
