Since it is a recessive gene, the only way that the parents would be 'symptomatic' is if they had two copies of the recessive gene. So basically, genetically, the parents could be like this:
Hen: Normal Eyes x hound dog
Cock: Normal Eyes x hound dog
So, since they only have one copy of the gene, the dominant 'normal' eye overcomes the recessive hound.
Now, the baby, if he has hound dog eyes, would look like this:
Baby: hound x hound
It would have NO instance of the dominant normal eye which means that to breed it out of the line, you would need to introduce 'teils that have normal eyes. It's possible that you could end up keeping the trait within the line, by inadvertently breeding birds with a single copy of the recessive gene. However, eventually, it should breed itself out as long as you were to choose birds with eyes that appear on the small side therefore possibly avoiding the chance of having a copy of the recessive gene.
It's been a while since I did anything with genetics (used to breed rats), but I know that the basic concepts are the same, and would presume that the way to breed out the undesired trait would be the same as well.