Poor little Carter Lake. It reminds me of the phrase, "a mystery wrapped inside an enigma" from the Oliver Stone film, 'JFK'. Carter Lake is a town in Iowa surrounded by a namesake oxbow lake that it doesn't own, then Nebraska, and finally, the sweeping curve of the Missouri River. It is the only town in Iowa that lies west of the Missouri River. According to Wikipedia, there was a flood in 1877 that redirected the course of the Missouri which left Carter Lake on the wrong side from that point on.
There are a number of strange borders in the US that are the result of river courses. When the initial borders were being drawn up, care was taken to not orphan small areas on the far side of a river that would make the area hard to govern. Bridges across major rivers were rare in those days and the natural boundaries of the rivers mattered. But rivers are dynamic and their courses are always changing particularly in flat, easily flooded land. I have already documented two other examples where this has happened, The "New Madrid Bend" border between Kentucky and Missouri and the winding border between the Louisiana and Mississippi along the Mississippi River near Vicksburg. If I was asked, I would suggest that a river border should stay a river border even if the river changes course. It seems like the natural recommendation. History has judged me wrong. Once a border has been staked out, human forces will act to keep it unchanged even as the underlying river seeks a new course. Since this land is often prone to flooding it is not usually prime real estate. Rarer still is the case of Carter Lake where a whole town occupies that changing landscape.
Omaha Nebraska lies just West of the map I've drawn. If you fly to Omaha, you land at Eppley Airfield. The strange border around Carter Lake creates a situation where, after landing in Nebraska, one must drive through Iowa to get back to Nebraska and the city of Omaha. As out-of-towners are often confused about directions, it must by particularly confusing to see the otherwise friendly signs in Carter Lake announcing, "Welcome to Iowa".