The apparently still field signed Hawaii Route 803:
https://www.gribblenation.org/2022/01/hawaii-route-803.html
According to hawaiihighways.com Hawaii Route 803 was at one point assigned as Honolulu County Route 803. It is unclear what the actual status of Hawaii Route 803 is given it is signed with modern Hawaii Route shields.
Hawaii county routes are usually signed (if at all) with route markers identical to state route markers. This is most obvious on Maui, Kauai, and Hawaii (Big Island) islands, which have many more numbered county routes than Oahu.
Hawaii used to have a combined route system, including both state- and county-maintained highways. Around 1968, separate systems were established for state and county routes, with some routes moved from one system to the other. Usually, this was the state fobbing off the worst routes (including the ones it had no plans to ever pave) on the counties. But up to 1968, route markers for both state- and county-maintained highways were all cutouts, so the remnant 803 markers you saw must've postdated the transfer of 803 to Honolulu County.
I found that and other history of the early post-statehood highway system(s) in Hawaii in the state library in Honolulu, and the 5th floor of the main University of Hawaii library. That UH library also had a map collection in the basement, including the Army Day map I photocopied, stitched together as best I could, and posted on my site. Regrettably, soon thereafter a rainstorm flooded the basement, destroying most or all of its contents.
I called the Honolulu County transportation department in the early 2000s, as I was revamping the Hawaii Highways site, about what was included in the county's numbered highway system. I was told that the county no longer maintained a numbered highway system. However, there is one county route (unsigned 7414, part of Middle Street in Honolulu) which was included in the state route log, perhaps because it was included in the National Highway System as a connector to the Ft. Shafter Army base.