Wait, something is missing! I can enable the palm check but there is no sensitivity adjustment. Naturally I checked the mouse properties control panel applet as well.
This was also useless. A search for the right ALPS touchpad driver ensued. Many Google searches and driver versions later I still did not have a solution. Then, finally, I discovered the secret. The controls aren’t in the applet, they are buried somewhere else! Just run
C:\Program Files\DellTPad\DellTPad.exe and this hidden executable will display all the settings that are missing.
I could not find a link or shortcut to this executable anywhere. Apparently you just have to know it is there. They couldn’t have made it any easier, right?