  The low-latitude globular clusters Terzan 10 and Djorgovski 1 are vprojected
in the Galactic bulge, in a Galactic region highly affected by extinction. A
discrepancy of a factor of ~2 exists in the literature in regards to the
distance determination of these clusters. We revisit the colour-magnitude
diagrams (CMDs) of these two globular clusters with the purpose of
disentangling their distance determination ambiguity and, for the first time,
of determining their orbits to identify whether or not they are part of the
bulge/bar region. We use Hubble Space Telescope CMDs, with the filters F606W
from ACS and F160W from WFC3 for Terzan 10, and F606W and F814W from ACS for
Djorgosvski~1, and combine them with the proper motions from Gaia Date Release
2. For the orbit integrations, we employed a steady Galactic model with bar.
For the first time the blue horizontal branch of these clusters is clearly
resolved. We obtain reliable distances of dSun = 10.3+-1.0 kpc and 9.3+-0.5 kpc
for Terzan 10, and Djorgovski 1 respectively, indicating that they are both
currently located in the bulge volume. From Gaia DR 2 proper motions, together
with our new distance determination and recent literature radial velocities, we
are able to show that the two sample clusters have typical halo orbits that are
passing by the bulge/bar region, but that they are not part of this component.
For the first time, halo intruders are identified in the bulge.
