I still get the heebie-jeebies thinking about it.
We're not quite sure what to do with it now. I'd like to give it a respectful burial, without causing a police response.
Unfortunately that's not an option.
A respectful burial means contacting the authorities so that the remains can be properly identified, and their final disposition noted in the public record. Remember this was once a human being, likely with many relations, however far back. The remains could be of someone entirely forgotten, but could be the missing link in some family's long and painfully sad story, also.
Meanwhile, the tail risk of getting into some kind of trouble for attempting to sidestep this necessary process is quite considerable.
So there's really only one course of action available to your father's heirs. Since there's also a small but considerable chance of being hit with some kind of charge (even if you do contact the authorities in perfectly good faith, and presuming of course that no hanky panky was involved in acquiring the skeleton on the first place), the first step will be to contact a criminal defense lawyer.
Quite some inheritance you were left with, there.
See also: https://www.npr.org/2024/10/25/nx-s1-5165150/skull-found-hou...
I really, really was sure you were going to just advise them, “just leave the skeleton in your closet forever.”
Once that happens, you have no control over their response.
That said, I absolutely recall seeing a documentary, in modern day, showing people's bodies used in science exhibits to this day. Their point was that while people had voluntarily donated their body to science, they were mostly unaware that this type of display was something that might happen.