Shouldn't really be any fat on a backstrap.....are you sure that's what you got?
Regardless, treat the straps exactly the same as tenderloin.....cut pieces 1 3/4" thick, Wrap with good bacon, roll the outside in coarsly ground black pepper, grill on high with the lid closed for 4 min a side, sprinkle with sea salt, let sit for 5 min and drizzle with a little butter (mince a clove of garlic into the butter if you'd like)
WW