Is it just me, but I feel like this being an NRO patch that the placement of the stars isn't just a designer's choice but potentially some cryptic meaning. If not, how boring!
Look up Trevor Paglen's book "I could tell you but then you would have to be destroyed by me". It's a collection of mission patches along with some interpretation as to the meaning and placement of symbols. Fascinating stuff.
My guess: there’s 3 stars that are brighter, and the cat is shown with 3 legs, so it could be part of a constellation of 3 satellites. The swoop of the tail could indicate a molyina orbit. Generally the orbit and where these things are in the sky can, and are, tracked even by hobbyists so that’s not particularly juicy, imo