Is there a launcher for that program in your start menu somewhere? Sometimes the icons in the sys-tool area don't show options, but opening up a config window from the start menu, (or install location on disk), will have an option that will take it away.
As for not wanting others to see your online... I agree with saltynay that most people would just open a web browser, (that is what I would do anyway).
If you just don't like seeing it in the system tray, you can always Manually force it to "hide" (while this just places it so that you have to click the arrow to see, it does get it out of sight.) to do this just adjust the configs in the taskbar panel. (right click on taskbar, properties, then in the customize by the "hide inactive icons" box, you can set it to "always hide"