Apple built iOS specifically with sandboxing, which means an app cannot affect System Settings. As soon as Duet has quit, it has no rights to execute code and cannot affect iOS or your hardware AT ALL.
Re-installing or uninstalling Duet on iOS generally has no effect – any issues with iOS outside of Duet are specifically related to the stability of iOS or your iDevice hardware. Any Apple employee, Apple Genius, or Apple support staff will confirm that Duet cannot affect the stability of your mobile device.
You can learn more about sandboxing here: