Who gave anyone the right to say what verse in the Bible will be 'accepted' and what verse will be 'rejected'?
I find it somewhat amazing that the very people who claim; "All scripture is inspired by God and is useful for teaching, for refutation, for correction, and for training in righteousness", are the very same people who claim that the Old Testament doesn't count!
Of course The Catholic Church following the example of Jesus and the Church that He founded on the Apostles [Eph 2:20], continue to count the teachings of the Old Testament when they are revealed in the New Testament.
For example; the teaching in question, on the necessity of being Holy to get into Heaven. Since both Jesus and His new Church taught and continue to teach Holiness is not option to our Salvation, we can refer to the teachings in the Old Testament that support Christ's teaching.
Another teaching would be what must we do to be saved?
Jesus answers this by telling us to keep the Commandments which are given to mankind in the Old Testament.
For further study on Dispensationalism see the article in "This Rock", published by Catholic Answers.
"Dispensationalism has its roots in the teaching of the English Plymouth Brethren preacher John Nelson Darby (1800-1882), but it was made most famous by the American preacher C. I. Scofield (1843-1921) who incorporated the system as part of a Bible translation in the Scofield Reference Bible. Dispensationalism teaches that God deals with man in seven dispensations in each of which man is set a specific test. This test continues as an abiding truth for successive generations."