Well this is a bug that has been there in Windows 8 and still persists in Windows 8.1 as well. At times the HomeGroup icon is displayed automatically on your desktop without your permission. Wondering how to delete it? Its very easy if you follow the 3 steps below.
Right Click on your Desktop and select the Personalize option.
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Now click on the Change Desktop Icons option displayed on the left.
If the box next to the Network is checked then uncheck it and then click on Apply or else check it and click on apply and then uncheck it again and apply to make this irritating icon to go away.
Also read: How to take screenshot in windows 8.1
Hope that Microsoft will fix this HomeGroup icon bug soon in their Windows 9 OS which is expected to be announced later this year. If you have any queries regarding this issue then please feel free to leave a comment below.