The area we now know as the state of Missouri wasn't part of the United States until the Louisiana Purchase in 1804. French and other settlers who moved into the area in the 1700s received grants of land from the colonial government of the time, whether Spanish or French.
A land survey was part of the process of obtaining a legal title. Surveys done prior to 1804 used a unit of measure called arpents instead of acres. Using a grid system was not required.
After the Louisiana Purchase, residents wanted to know if their claims to land would remain valid. The US government set up a board of land commissioners that took more than 50 years to review all the claims, by which time many of the original claimants were deceased.
This detail of a page from the 1862 plat book of St. Louis County shows the contrast between the square grids used by the US government and the irregular shapes of earlier land surveys.
The north portions of sections 6 and 5 in the map on the left were owned by Edward Bredell. He bought the land after the US surveyed it. The US used a square grid system of townships and ranges to survey public lands.
The parcel owned by Leonard Farrah crosses sections 5, 4, 8, and 9 at a diagonal. It doesn't fit the grid—a clue that it's a parcel of land surveyed under the French and Spanish colonial governments, before Missouri became part of the United States.