This GIF is made (via giphy.com) from the new NAASA Goddard video Hubble's New Image of Interstellar Object. It shows the comet moving at quite a clip!
This shouldn't be a surprise.
From the link in the question https://archive.stsci.edu/proposal_search.php?mission=hst&id=16009 the coordinates for the first and last exposure are:
RA Dec Time
09 47 45.181 +18 07 30.70 2019-10-12 13:44:39
09 48 17.077 +17 59 20.37 2019-10-12 20:42:23
In 7 hours the comet moved roughly 0.2 degrees!
From JPL's Horizons, the state vectors for the comet and Earth around the middle of the image sequence are:
JDTDB Calendar Date (TDB) X (km) Y Z VX (km/s) VY VZ
comet 2458769.250, 2019-Oct-12 18:00:00, -1.9092457E+08, 2.9804744E+08, 3.2507629E+07, -1.3003446E+01, -2.9440986E+01, -2.7477326E+01
Earth 2458769.250, 2019-Oct-12 18:00:00, 1.4082817E+08, 4.9358841E+07, -1.4600024E+03, -1.0121471E+01, 2.8065445E+01, -7.7695706E-04
The comet is about 416 million km from Earth, moving at roughly 64 km/s relative to Earth and 42 km/s relative to the solar system barycenter.