Dolly,

The Catholic Church doesn't teach anything about repetitive prayer as such; she does recommend the rosary and other such prayers but generally they are coupled with meditations on the mysteries of the faith. So, they aren't bare repetitive prayers. They are primarily intended to meditate on a truth; the repetition is just the backdrop and makes it easier to meditate because you don't have to think about what you're going to say.

In the Rosary, there are five Mysteries you meditate on, different aspects of the Gospel or important events associated with it.

We can see examples of repetitive prayer in the Scriptures. For example, in Psalm 136, the phrase, "for his love [or mercy] endures forever" is repeated after every line for all 22 verses. That's almost half the number of Hail Mary's in a Rosary!

Where this objection is rooted is in Matthew 6:7 which says, “And in praying do not heap up empty phrases as the Gentiles do; for they think that they will be heard for their many words.” (Matthew 6:7, NRSVCE or RSV2CE) (Ironically, this is where Matthew introduces the Lord's Prayer, one of those repeated prayers of the Rosary people object to.) 

Examples of pagans actually doing this are in 1 Kings 18:26 and Acts 19:34, where the pagans repeat a short invocation of their god in hopes of god hearing, thinking that by repeating the invocation, they are wearing their god down to do their will. This is far from the attitude of the Catholic, who in the Lord's Prayer fulfills the will of Christ and in the Hail Mary, it evokes the Incarnation of God which is so centrally important to our faith as Christians.

I'll note that the Rosary is of fixed length. There is no sense of trying to "wear down" God by invoking him until he answers. They are not "empty" phrases (or "vain" repetitions) because they are imbued with meaning and purpose. The Greek has the sense of babbling or stammering, which again is far from the reverent recollection of the Incarnation in the Hail Mary or the comprehensive petitions of the Lord's Prayer.