Your best bet for determining which aircraft this came from is probably to look for a stamped number somewhere on the part and do a search by National Stock Number.
These parts do wear out after some number of arrested landings, and once the hook point fails inspection with a Go/No-Go gauge they are scrapped. At sea they are likely to be pitched overboard, while ashore they would likely end up in a scrap bin somewhere.
Military bases used to have a local Defense Reutilization Marketing Office, (DRMO) where civilians could go to purchase surplus military items, but these sort of activities have been largely consolidated under the Defense Logistics Agency, (DLA).
Items with some purpose are evaluated, de-milled if required, and either dispositioned for auction or disposal. With such a specialized function, (and being on the munitions list as I point out below...) it is highly unlikely that tail hooks are ever offered to the public. Any person in possession of one likely got it outside of approved channels.
While obtaining a tail hook outside of DLA would run afoul of normal administrative procedures, it is very unlikely that simply having one in your possession would be illegal, especially if it was acquired in the course of a legal property transaction vs getting caught dumpster diving on base.
If you were to sell it, however, it would be illegal to export under current Export Administration Regulations, (EAR).
Title 22, Chapter 1, Subchapter M, Part 121.1, of the United States Munitions List, under Category VIII—Aircraft and Related Articles, sub-section (h) states:
(1) Parts, components, accessories, and attachments specially designed for the following U.S.-origin aircraft: The B–1B, B–2, B–21, F–15SE, F/A–18 E/F, EA–18G, F–22, F–35, and future variants thereof; or the F–117 or U.S. Government technology demonstrators. Parts, components, accessories, and attachments of the F–15SE and F/A–18 E/F that are common to earlier models of these aircraft, unless listed in paragraph (h) of this category, are subject to the EAR.
It goes on to specify in more detail:
(5) On-aircraft arresting gear (e.g., tail hooks and drag chutes) and specially designed parts and components therefor
It is worth noting that the aircraft models listed are all in the current US DoD inventory, so it is very possible this restriction will be lifted once the aircraft are decommissioned.
P.S. Regarding your since deleted bullet about value, I actually messaged the guy asking $24K to ask how he came up with this price since it's identical to one I have. He laughed and said he didn't really want to get rid of it for sentimental reasons, but that he would take that for it. So your comparison does not make for a fair estimate with something as niche as this. And market value only has any meaning when there is a transaction to prove someone will pay some amount.