I would not want my children to get their hands on a non Catholic book personally. I have not directly received a bible, but have gotten some pamphlets and defintely throw them away. I don't think that is such a bad thing. I am nice about it and don't do it in front of them at all.
Most RCC believers I know have found the Holy Bible to be on eif not the most Catholic book they might ever procure.
You throw the Word of God away in front of God. You can't get out of His view.