Hi, I can help.
I have a roo who is clearly barred (he was supposed to be a pure barred rock but isn't) he has one copy of barring. I want barred offspring but he only passes it to half his children. If you don't want it it's easy to deal with. Keep the pretty roo or roos you want to use. Breed them and look over the offspring. If the roo does carry a copy of barring half of his children will not have it and you can select from them.
If you think neither of the parents of your birds had barring but some roos clearly do, check over the mother hens carefully. More than likely one of them is carrying it and passing it on to her sons. It can be very hard to see sometimes in females, especially on a hen with gold base and a pattern which is exactly what your breeding for. See below.
Thankfully barring is very easy to get rid of because it's dominant and you can easily cull any offspring that have it.
Also, it's possible to get faint 'barring' on feathers simply due to changes in diet or stress or other things when they are growing. That isn't true barring and usually disappears after the next moult.
Edit: Pics
Please excuse quality, my camera died and I had to use my phone. These birds have a lot going on color wise so I completely understand what you mean with barely there barring.
A barred gold pullet with some mottling. Her barring is very difficult to see.
Pullet left, the cockerel right. Both barred but it's much harder to see on the pullet.
These are all siblings, you can see only half have barring.
