You can breed it out with a lot of effort, but it won't just disappear unless you're very lucky. Each bird carrying a recessive trait has a 50-50 shot of passing that trait on. If they're bred to a bird who is not hiding that recessive trait, then their offspring will look like they should, even though half of them carry the gene and there are no outward signs of which do and which don't. Each of those birds is essentially a coin flip whether or not they have it. So you can luck out and just happen to pick the right birds to eliminate the trait, but odds are pretty high it'll haunt you for a long time before that ever happens.
You can also test cross your birds and only keep the ones that confirmed are not carrying the recessive genes through that. However, test crossing takes a lot of time and space, and you end up with a bunch of mixed birds you don't want or need as a result of it.
I've also heard of DNA testing for certain genes, but I don't know if comb genes are one such set of genes that can be tested for, nor where to look to find out.