A good tile installer that knows what he is doing, can easily remove that single piece of tile.... carefully replace it with another one. Do you have another extra pieces of the same tile? Do you know what brand and color the existing grout is? That will be more of the issue trying to get the grout match to match up or the finding the same tile (in the same dye lot) if you need to buy another tile. Did the heat cause the break or did a pan bang into the glass? Consider installing a heat resistant Lumicor or 3 Form panel behind the stove. Any flat material that can be sandwiched between two resin panels. 1). Crushed glass. 2). Fabric. 3). Fabric. 4). Fabric.

If you love the marble tile, go for it! You can always buy a stainless or white range hood backsplash like this http://www.wayfair.com/Air-King-Range-Hood-Back-Splash-SP2430-AXK1174.html to slip in place when you are cooking something really messy. I have a travertine backsplash and use a stainless sheet when frying. It works great and no worries about stains ruining the stone.

@Rock Doc: Are you addressing this to me? I haven't actually bought these tiles yet - when I do, I will definitely be going for the handmade ones. They're a work of art and irreplaceable in my opinion. However, there are also screen-printed tiles available in the market in more or less the same patterns; the workmanship is of course different, but you get them cheaper, and they're also more easily available. You could give that a shot. I'd recommend Aakaar Flooring Solutions - they're here on Houzz and are able to provide both the above-mentioned types.

Greetings from Dream Design, As per your inputs we suggest some ideas -Don't go with too dark backsplash as it will make the kitchen dull after some time and kitchen will look smaller -You can go with marble/tile or even the same counter top like quartz if you use in counter top you can same also put in backsplash as currently it's in trend -take white color with some black/grey lines marble or quartz -or you can go with white designer lines with grooving Sharing some reference pictures