You have an extended micrometer sight, similar to the type usually found on match 22LR rifles. That said, it looks awful crude and has kind of a Soviet or Chinese look to it (maybe off of a cheap biathlon trainer rifle like the ones that appeared in the 1990s?). The base fits the drilled/tapped holes in the side of the receiver, and the peep sight itself is adjustable for the distance it extends towards the shooter. I think it would be a good sight for what you are talking about, many of the 340s were drilled/tapped at the rear for peeps.
Never try to educate someone who resists knowledge at all costs.
But what do I know?