Of course you can remove them but remember that the arrow means it's a shortcut while no arrow means it's a file in the desktop folder. If you remove it you won't be able to tell the difference - Careful what you delete......
I agree with Patr100 about not knowing which are shortcuts and which are file icons. I have on numerous ocasions (In Win 98)deleted what I thought was a shortcut, only to find I had deleted the file. Also when copying a file I have copied the icon instead of the file. When I had deleted the (file)icon I found that I had only a useless icon instead of the file.
My advice is to leave them as they are. I do now and I have not made that mistake since. Be warned.
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