Zahra,
A DNA test would reveal whether one is a beta+ or a beta 0. Beta 0 simply means that both beta genes are serious deletions or mutations resulting in no or minute ability to produce beta globulin chains. Beta+ means that one or both genes have a mutation that results in some production of beta globulin - meaning that the patients are capable of making some hemolobin on their own, albeit not enough to be transfusion independent.
At this stage, gene therapy is able to increase hemoglobin enough to completely cure beta+ because the new genes are able to increase the hemoglobin by around 5.2 (more or less in some patients) and beta+ patients are able to make some hemoglobin resulting in a complete cure. Beta 0 patients produce no hemoglobin and at this time the gene therapy is able to increase their hemoglobin significantly but not to a level where they are completely transfusion independent. It is early in the trials - it is possible that over time these patients will begin to produce more hemoglobin with the new gene - otherwise further revisions in the procedure will help them perfect the technique such that beta 0 patients will reach high enough hemoglobin levels to be completely cured.
Remember this is the first attempt at gene therapy and an increase of hemoglobin by 5 points is excellent. The point is that it works! With gene therapy thalassemics can make blood. Now the process must be refined to produce the right amount.