how get rid of grayed out safari symbol on my mac desktop

If you have somehow moved the actual Application, Safari.app, to the desktop, it will never execute from there. It must be put back, or you may need to re-install MacOS.

If it is actually an Alias to Safari -- with a little arrow in the corner of the icon -- (and the original is still in the /Applications folder where it belongs) just drag the Alias to the Trash.