I just re-read Synthesis "Imprint: Guardsman" and the second half really reminds me of ant hierarchies.
Most species of ants have a single queen giving birth to ants non-stop. That is more or less their sole purpose in the ant colony. The moniker of "queen," however, has no practical basis wrt human royalty; any given queen is simply yet another member of the colony performing her job and all the worker and solider ants protect the queen ant solely for the good of the colony.
There are some species that can have multiple queens per colony. In some of these multi-queen colonies, the worker castes have been seen literally tearing apart queens of their own colony (possibly to purge unproductive queen ants or perhaps excess ones , as queen ants take a lot of the colony's energy and supplies to care for).
Simply put, a "queen" ant isn't in any particular way regal or royal. They are simply another type of cog in the machine of a colony, albeit a proportionally miniscule cog.
Judging by the story, I feel like Grineer society is similar.
It's established that Bilsa is Sectarus class Orokin and as such, has special privileges through gene-locked security systems, ex. ship Cephalon access. The central conflict goes on to outline how important her security privileges are during the events of the story. With the Orokin Empire collapsed, all social pleasantries have evaporated and now her status as Sectarus is a coveted asset -- Alarez is lower-ranking in the Orokin Empire hierarchy but clearly no longer respects whatever social rules had previously protected Bilsa and now Dax and handling her like a key resource than a person of high social stature.
Similarly, although Veytok, his Grineer, and Bilsa have come to an "understanding," Veytok does not oblige Bilsa's request to capture Alarez alive as one might expect a person of lower social rank to heed a person of higher rank. Nonetheless, Veytok ambushed Alarez, protecting Bilsa.
When Veytok grunts "You are Gineer now, don't need visits" that very much reminds me of ant colonies. The worker and soldier castes work, fight, and protect the queen ant, but ultimately, the queen ant holds no special authority over the other ants -- the colony is a system and each caste (including the queen caste) is a part of the system, working together to continue the reproductive cycle of the species. So I draw a parallel between ant colony organization and the Grineer. The working Grineer and the soldiers protect Bilsa, but not because she is royalty. The Grineer protect Bilsa because she is valuable asset to the burgeoning Grineer faction. The Grineer need Bilsa to access Orokin technology so they can protect themselves, further their interests, and reproduce (i.e. cloning), while Bilsa depends on the Grineer to protect her. She and the Grineer form a higher form of "Grineer," in which this higher form of Grineer is composed of interdependent elements.
The Grineer empire in the context of the short story reminds me of an ant colony. The end.