This question has subject verb agreement error. Since a recent spate is the subject, has should be used and not have. Hence we are left with C,D and E. In C its cannot refer to the diets and hence the usage is wrong. In E convince should be followed by an infinitive or that. Hence answer is D.
A.have done little to convince its practitioners that they should follow more traditional weight-loss plans
B.have done little to convince their practitioners to follow more traditional weight-loss plans
C.
...
A.have done little to convince its practitioners that they should follow more traditional weight-loss plans
B.have done little to convince their practitioners to follow more traditional weight-loss plans
C.
...

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