  We use multiband archival HST observations to measure the photometric and
structural parameters of the M81 globular cluster that hosts the Fast Radio
Burst FRB 20200120E. Our best-fitting King model has an effective radius $r_h =
3.06$ pc with a moderate King model concentration of $c = 53$, and an inferred
core radius of 0.81 pc. We revisit the exact astrometric location of the FRB
within the cluster, and find that FRB 20200120E is located 1.92 pc from the
center, but within the projected half-light radius. We estimate the relative
encounter rate of the FRB host, along with the corresponding rates of 210 other
globular clusters in M81, and compare these values with the encounter rates of
Galactic globular clusters. The FRB resides in a globular cluster with an
encounter rate that is moderately higher than the median stellar encounter rate
in our two comparison samples. While the estimated encounter rate of the FRB
host cluster (e.g., $\sim50\%$ of a cluster like 47 Tuc) is sufficient to allow
the possibility that the FRB formed dynamically, our results do not place
strong constraints on this scenario due to the limitations of the available HST
data and the possible systematic uncertainties and selection effects in the
comparison data.
