First of all, sorry for the confusing original image. It comes from foreflight and has three charts superimposed. 1) the sectional, 2) the houston helicopter route chart (white background) and 3) the foreflight aeronautical chart showing the airpace again. I'm attaching a simpler one which shows just the sectional and the helicopter route chart.
It turns out that the helicopter route chart is simply out of date (!?). I called the Sugarland tower and they confirmed that 2 years ago the Delta expanded from a 4.2 mile radius to a 5 mile radius. The Helicopter route chart still depicts this as 4.2 (https://aeronav.faa.gov/content/aeronav/heli_files/PDFs/Houston_Heli_9_P.pdf) Hopefully the next edition will correct this.