Meat – When does the rule “only flip meat once” not apply

I believe it is kind of like the difference between broiling and baking. "Open top grill" only cooks from underneath (kind of like broiling but not from above). Baked or "covered" grill will distribute the heat more evenly.

For more information see: http://www.epicurious.com/articlesguides/howtocook/primers/grilling_lightingandgrilling

That's where I double checked my assumption and got the metaphor of broiling and baking.

Cook it with the string on, then remove the string when you eat it. It is there to hold it altogether while cooking. Should be fine to grill, butcher's twine is food safe and stands up to roasting and braising so should be fine on the grill too. But if you wanted to do something else, like turn the smaller pieces into kabobs, then you could skewer them with some veggies and grill them.

At least your butcher was honest about tying the pieces together with string. I bought a vaccum packed ribeye "steak" the other day and when I was grilling it and turned it, the top part came off as a thin slice like roladen.