Just a clarification on the grounds of terminology, but a martingale is a leather loop that is attached between the grip and the guard and is usually found on French grips; the fencer pus their four fingers into the loop when they grasp the weapon, the point being, back in the days of non-electric fencing, if they were to be disarmed the weapon wouldn't go flying about.
The retention device used with an Italian grip in the traditional Southern Italian fencing style is simply referred to as a wrist strap (there's an Italian word for it, but it escapes me at the moment).
Also, how is the crossbar twisting your fingers? Are you holding it as depicted in the pictures attached in
this post?