Funny display spot - what can it be?

I've just discovered something on the screen of my laptop that looks like I've greased something sticky there, like touching Ewas with sticky hands, it's not a really eye-catching stain, just looking a little darker. With the screen off, it looks more like a small grease stain. What could that be? You can't get rid of it.

If it looks like a grease stain, it could be a grease stain.

Maybe you hit a fly when you closed it.