I have installed "not signed by Microsoft" driver for my
USB modem. The driver is fine, I just want to know how to
disable "uninstall hardware" icon (green arrow) now
permanently located in my Task Bar. Thanks.

You could try to just hide the menace icon by going to the
taskbar properties, selecting "hide inactive icons," then
clicking "customize," then choosing to permanently hide
that icon.
As for uninstalling the icon, doing that is a really
sticky business. I wouldn't try it.