for a backsplash it should be sealed, but doesn't have to be honed. polished marble repels stains just a tad better than honed, but will show scratches easier. since it's a splash, that probably won't matter.

sealing penetrates the stone and offers a barrier. anything acidic (tomato sauce, lemons, vinegar, etc) will etch (basically leaves a dull spot) which will show on polished worse than honed. sealing will not prevent this. sealing will give you time to wipe off the tomato sauce before it sets in and discolors the stone.

you need an impregnating sealer meant for marble. honed marble requires a sealer meant for honed stone. I used Aquamix Gold, water base sealer for my honed marble on my floor. it took 2-3 coats. wait until it's installed/grouted and until all moisture is evaporated. about a week or so. then apply the sealer per the instructions. you may have to do it twice. then every 6months to a year, reapply. you will know when it's time to seal when water no longer beads up on the stone but gets absorbed.

sometimes the tile installer will do it, but I like to wait until all the moisture is dried before applying. Some say you don't have to, but I do. so if the installer will be charging you extra to do it, say no and do it yourself. it will take 10 mins and maybe $35.

You MUST seal. And be prepared for grease spatter..........impossible to remove sometimes, even WITH a good seal. Ideally, seal very well PRIOR to installation and then again as Beth above. Grease/oil is a much bigger issue on honed marble.