Do Muslims say this to make it sound more appealing to Christians? Or is it really the final testament?
Muslims believe that the contents of the Qu’ran were revealed to Mohammed in the sixth century A.D. That is why they call it the “final testament,” because it is alleged to be a revelation of God given after the Bible. Christians, of course, do not believe this, but believe that general divine revelation ended with the death of the last surviving apostle (usually believed to have been the Apostle John) around the end of the first century A.D.
The Catechism of the Catholic Church states:
Throughout the ages, there have been so-called “private” revelations, some of which have been recognized by the authority of the Church. They do not belong, however, to the deposit of faith. It is not their role to improve or complete Christ’s definitive revelation, but to help live more fully by it in a certain period of history. Guided by the Magisterium of the Church, the sensus fidelium knows how to discern and welcome in these revelations whatever constitutes an authentic call of Christ or his saints to the Church.
Christian faith cannot accept “revelations” that claim to surpass or correct the revelation of which Christ is the fulfillment, as is the case in certain non-Christian religions and also in certain recent sects which base themselves on such “revelations” (CCC 67).