Using the Control Panel -> Change Installation (Windows 7 Pro 64-bit) option, I removed the desktop gadget option from installation. On restart, it was not uninstalled or removed! More time wasted and my opinion of Avast falls further.
As I said before, this is an unrequested annoyance.
If I am unable to easily remove the desktop gadget, I will uninstall Avast, and next time, I will definitely reconsider whether or not I want to go with a company that attaches annoyances such as this to their installations.