What is the Catholic stance on Embryo Screening? Embryo Screening is the process of fertilizing multiple eggs, checking their DNA makeup, and then screening out the eggs that do not meet the requirements.  These requirements can be anything from potential health issues (genetic diseases) to gender preference.

Obviously, the Bible doesn't have much to say about this directly.  Still, I'm curious what the Catholic stance is for or against this and what Bible verses support this stance.
This looks like a case for Evangelium Vitae: 


  Special attention must be given to evaluating the morality of prenatal diagnostic techniques which enable the early detection of possible anomalies in the unborn child. In view of the complexity of these techniques, an accurate and systematic moral judgment is necessary. When they do not involve disproportionate risks for the child and the mother, and are meant to make possible early therapy or even to favour a serene and informed acceptance of the child not yet born, these techniques are morally licit. But since the possibilities of prenatal therapy are today still limited, it not infrequently happens that these techniques are used with a eugenic intention which accepts selective abortion in order to prevent the birth of children affected by various types of anomalies. Such an attitude is shameful and utterly reprehensible, since it presumes to measure the value of a human life only within the parameters of "normality" and physical well-being, thus opening the way to legitimizing infanticide and euthanasia as well.


It applies specifically to already implanted/natural conceived children, but ought to be widened to your case given today's technology.  We'd consider those children to be just as fit for life regardless of their genetic defects.  In fact, the very idea that they have genetic defects when barely conceived should make it more obvious that they are fully human!

If you want a biblical basis try:


  It is I who bring both death and life


(Dt 32:39)

which is to say, don't play God.