I'm going to say that it depends on the clan the unit is from. I'll mention that at this point in time the trials clans are doing are beginning to get larger, so the equivalent of 4 stars for access to the matrilineal genetic material of a strong exclusive bloodname might be a bit small.
Re: territory/lower caste enclaves
The Coyotes and Hellions both have enclaves on the following worlds: Babylon, Foster, New Kent, and possibly Londerholm. These allow for easy and quickly repeated trials to capture territory or production facilities (Babylon has a pair of Hellion controlled ASF factories).
The Fire Mandrills and Hellions both have enclaves on the following worlds: Atreus, Foster, and Marshall.
The Cloud Cobras and Hellions both have enclaves on Babylon, and can go after their facilities there. This actually supports the clan quite nicely materially as the Cobras are noted as having very heavy aerospace assets.
The Hell's Horses and Hellions don't appear to share a world, but they very well might go for a year's worth of production from a manufacturing facility or four - these are among the less likely to go for territorial gains.
The Smoke Jaguars and Hellions share Atreus, Foster, and Londerholm. They are probably the most likely to target production as they know they aren't doing really well materially, also the least likely to go after genetic material as they don't hardly use the material they have access to anyways.
The Snow Ravens were booted off Marshall, but otherwise don't seem to share a world. They may be the most likely to go after genetic material to show their own strength.
Any of the above could certainly target Hector, but going after territory there is probably going to provoke an inordinate response that your little unit is unlikely to be able to match - and harvest trials aren't really a thing yet so are also unlikely to occur.
If one is to look at what the unit can reasonably attain, it is probably going to be production, materials, territory, patrilineal genetic material or non-exclusive low level matrilineal genetic material. Odds are the unit is too small for a territorial attack on Hector, or to attain access to genetic material to a higher level exclusive matrilineal line - 5 or 6 years earlier and this might have been more likely.
A note about definitions since I'm not 100% sure I'm using the right ones. I am using patrilineal to refer to genetic material which cannot be used to determine bloodname availability, and matrilineal to refer to genetic material which can be used to determine bloodname availability.