Well, since we have the Knights Who Say "Ni!", and maybe the Black Knight too, it's clear this place isn't just a one-knight stand.
Not to derail the discussion beyond what has already occurred, but just remember that every populated non-interdicted Imperial world always has at least on Knight associated with it:
https://travellermap.com/?options=58363&p=34.191!41.462!8.35
https://travellermap.com/?sx=-1&sy=-1&hx=25&hy=8&world=Nii&p=-7.338!72.47!8.8&options=58363
In this regard, Tremous Dex is more like the worlds of District 268.
Where the Duchess of Glisten has responsibility to advance Imperial interests in Dist 268, One would assume there is an Imperial Noble who has the same role with the neutral zone.
Not withstanding the fact the armistice after the 3FW kicked the Imperial border back and designated it as neutral space, there will be an interest. I would expect the noble in charge to be the Duke of the Vilis Subsector (Bondal a'Plena, per the OTU Canon)
This because Regina already has control over the County of Jewell and is astrographically too far away. Because the County of Jewell is only a County, and has some level of administration from Regina, I would not assume it would hold sway over the Full Duchy in Vilis subsector.
That said, even if the persons are not recognized by the local worlds as more than an Ambassador, there might be Imperial nobility who hold responsibility for each independant world in the subsector