According to this tutorial, it is possible to delete a secret, by running:
vault delete secret/hello
What will if someone in the organization accidentally removed a secret. Is it still possible to recover this?
If your secret backend is a separate service, which it should be, then with regular backups you should be able to stop vault, replace the backend with a backup and be good to go.
I've done this for a file backend but don't know what would happen for other backends so ymmv.