We have the end of a 4" granite splash in our bathroom that is unpolished. We are getting ready to put the house on the market so I'd like to be able to polish the end of that granite so it matches the rest of the backsplash. Is there a quick and easy way to do that without taking the backsplash off?

Yes, but the investment in tools is probably more than you're willing to spend.

For looks, I'd find some wet look sealer, even some spray urethane, and use that to make the dull cut blend with the glossy surface.

You can polish edges with a grinder and various grits of materials - but it might not be worth the cost if you don't have everything you need. And you would probably have to patch/repaint the sheetrock next to it afterward.

Have you thought about just applying some clear finish (epoxy, etc.) to the end so the color matches the finished sides?