Okay, this confused me a bit..Remember that the barred gene is sex linked. A rooster gets a copy from both his parents but the hen only gets a copy from her father.
So the first generation of a barred rooster over a non-barred hen, the boys will be split for the barring but all the girls will be barred. So you have to keep one of these roosters to get rid of the barring. But you have two choices on the hens.
You can put that rooster over the Jersey Giant hen. Half the offspring, male and female, will be barred and half will not. These are just odds of course not real results. I've had 4 out of 4 barred from this type of cross. What you actually get is just luck!
If you breed that rooster back to his sisters, all the boys will have barring. They'll get that from their mother. You really won't know if the boys have two barred genes or not. You can make a pretty good guess because the boys with double barring will be lighter in color than the ones split for the barring, but that is just an educated guess. You may hatch nothing but double barred roosters.
So if you keep the non-barred hens from this generation and mate them back to their father who you know is split for the barred gene, half their offspring, male and female, will be barred and half will not. This is the generation where you can eliminate all the barring.