Remove "Show Desktop" button next to the clock in Windows 7
7+ Taskbar Tweaker provides this option among many others. It's a robust little program that I've been using for quite some time without a problem. It adds exciting new functionality to the Windows 7 and Windows 8 taskbar and fixes some of its flaws.
I don't think you can remove the button, but you can disable its functionality. Right-click on Superbar -> Properties -> uncheck "Preview desktop with Aero Peek"
Sorry it seems that beyond this, there is no way to remove it.
Quotes:
Microsoft Technet:
Hi,
Based on my research, there was no related article about the feature. I suspect it is by design and you cannot remove it.
Seven Forums
There is no way to do it.
HardOCP
As far as I know, it cant be removed. you all will just have to live with it.
This tool should be worked. I have tried it.
http://www.thewindowsclub.com/remove-and-restore-show-desktop-button-with-showdesktop-remover