Hi,
Yes that is exactly how you remove it.
Any animal expressing it gets removed from the genepool for the next generation.
Depending on the genepool you start with containing the traits you do want you might be forced to re-breed the parents - you will also want to find out the genetic inheritability of the bad gene as well.
No point in removing visuals and discovering it was a recessive trait and you now have a whole generation of hets for example.
Removing genes is just as complicated as adding them to make that dream morph combo - if not more so as absence of proof is not the same as proof of absence.
Hybrid vigour comes back to the genetic variation available to combat diseases or problems affecting the species so yes, it could become a problem.
Lack of it in the wild could be devastating to a species.
In captivity we have to ask if we could medicate, innoculate or otherwise interfere with the problem - we have with every other species we keep after all, including humans.
dr del