If you want to delete the icon, there is many solution but mine is not the better, it seem to be a trick:
copy all of this icon to another directory may be your home.
write two script.
one will delete the icon, this one will run when you login to gnome.
another is to copy the icon from the backup directory back to your desktop, this one will run when you login to KDE.
I think this trick will work, but there must be something easier.
I use the full version of Gnome.
The KDE's icon also appear on my desktop.
when I change the icon in Gnome, it is also change in KDE since they are the same.
But there is only one icon (in KDE is have 4, so 3 is virtual).
It is the shorcut to the KDE recycle bin (Gnome does have it own recycle bin).
Since I used Gnome most of the time, I don't need to delete the icon.
I moved it to the edge of the screen and forget it.