  Directly-imaged planetary-mass companions offer unique opportunities in
atmospheric studies of exoplanets. They share characteristics of both brown
dwarfs and transiting exoplanets, therefore, are critical for connecting
atmospheric characterizations for these objects. Rotational phase mapping is a
powerful technique to constrain the condensate cloud properties in ultra-cool
atmospheres. Applying this technique to directly-imaged planetary-mass
companions will be extremely valuable for constraining cloud models in low mass
and surface gravity atmospheres and for determining the rotation rate and
angular momentum of substellar companions. Here, we present Hubble Space
Telescope Wide Field Camera 3 near-infrared time-resolved photometry for three
planetary-mass companions, AB Pic B, 2M0122B, and 2M1207b. Using two-roll
differential imaging and hybrid point spread function modeling, we achieve
sub-percent photometric precision for all three observations. We find tentative
modulations ($<\!\!2\sigma$) for AB Pic B and 2M0122B but cannot reach
conclusive results on 2M1207b due to strong systematics. The relatively low
significance of the modulation measurements cannot rule out the hypothesis that
these planetary-mass companions have the same vertical cloud structures as
brown dwarfs. Our rotation rate measurements, combined with archival period
measurements of planetary-mass companions and brown dwarfs do not support a
universal mass-rotation relation. The high precision of our observations and
the high occurrence rates of variable low-surface gravity objects encourage
high-contrast time-resolved observations with the James Webb Space Telescope.
