I have this tripod, and use a replacement head with it. JRP is correct in his assessment. You purchased the wrong replacement bolt. My RRS head would have problems with the stud you purchased as well.
The correct Gitzo bolt is the Gitzo D01.110 replacement stud. Among other places it's sold by RRS.
JRP's solution to use the Markins Titanium Stud 3/8", 0.82" (20 mm) long 3/8"-16 threaded stud is on the money and will work perfectly. I'd go with the Markins Titanium Stud if it were me, since you're using the Markins head.
It's recommended to use a thread locking liquid such as Loctite 277 when you use either of these studs. Personally, because you're putting it on the Gitzo Traveler 2 legs, where you might want to take off the head while traveling (I do.) to either make the overall package shorter, or prevent the theft of the ball head if you pack the legs in your checked in luggage, I wouldn't use a thread locking liquid.
I suggest using a nut on the stud to lock it in place when in use. This will allow easy removal of the head while in transit.
MONSTER TIP: If you don't use a thread locking liquid make sure you remove the stud from the head and the traveler's column while in transit. If you don't, you will probably find the stud has wormed its way down the column and may need to be extracted from the tripod. You absolutely don't want that to happen.