Why have some protected areas in the US holes?

Why have some protected areas in the US rectangular holes? I’ve found this

in Montana:

and in Utah:

This hole for example has another ownership: state vs national

This is typically because those holes are privately owned, as opposed to owned by the government. These large chunks of land are bought up piece at a time, and private properties are frequently landlocked inside large public land parcels. This is very common with BLM land out west and fairly common with National Forest land in the east.

These are often called “inholdings” and are usually private property which is not part of the public land. Often, there is a “human improvement” on this property (like a residence, perhaps outbuildings such as barns for livestock or farmyard storage), however this isn’t required or always true. However, it IS true that the “inholding” is NOT part of the public land.