I also just got an Italia strap and found the leather to be a bit thick, but the hole was the right size, and I managed to get it on my Les Paul. After a few on and offs, it has broken in a bit, and I believe will be fine after a few dozen passes. The quality of the leather, IMO, is pretty poor, but the workmanship is decent, and it's hard to beat the price. Still, no doubt my Moody strap is much nicer.
It's easy to enlarge the hole, or just the slit off the hole, if you need to.