The NYPD sees itself as an occupying force in a hostile city. What they've lost (or believe they've lost) is the respect of the natives; rather than questioning why that is, they've decided that the appropriate course of action is to extract all the value they can from the city while diminishing the natives' qualities of life to the greatest extent possible. Revanchism is the appropriate descriptor.
Again what loss do they to avenge exactly?
[1] https://www.bloomberg.com/news/articles/2023-03-20/nypd-blow...
[2] https://www.bloomberg.com/graphics/2021-nyc-police-overtime-...
> What they've lost (or believe they've lost) is the respect of the natives;
I don't know why you're performing such a hostile reading: it can be simultaneously true that tension for police and residents has been present for decades, and that the police have shed a degree of respect and baseline approval that they've historically held[1], regardless of whether that approval was ever actually justified.
Which is what has happened[2].
[1]: https://www.ojp.gov/pdffiles1/nij/grants/205619.pdf
[2]: https://www.nytimes.com/2020/08/12/us/gallup-poll-police.htm...
The euphemism was more subtle, but is also a known one[2].
I'm sorry if you found either confusing; that wasn't my goal.