For those lost souls seeking closure on this, and I'm sure there are hundreds of you, here it is:
I finally figured out where the heck this dialer come from (no thanks to the app's translator, who was only willing to tell me I'm using the old version... which I'm not!).
As soon as you install "360 Guards", it creates this icon on your desktop called "Fast Dialer". So one might wonder where it came from, because 360 Guards is mainly a security program, and has absolutely no relation to contacts and dialing apps. Nor does it warn you its going to create a dialer shortcut for you. Now here's what I missed... deep deep within the program, and its 500 settings, there is a box named "Createdspeed dial icons in desk". Which creates the Fast Dialer shortcut. But because it is a shortcut created within an app, and not an app itself, there is no way to change its icon, as far as I know. (For this reason, I have decided to abandon the dialer, good as it is. As it breaks my icon theme....).
Say goodnight, Gracie...