From the study you linked:

> Our study has limitations. First, detection of an interaction effect requires a large sample size. The present findings require replication with a larger sample of trials designed to test the interaction. The trials from which the data were extracted were not designed to test this hypothesis, but do provide a ‘first look’ into this question using all available data. Given the wide confidence interval around zero for the interaction coefficient in the present study, it is possible that our finding represents a type II error. Although none of the sensitivity analyses were suggestive of possible interaction effects, future studies may nonetheless still reveal an interaction that we failed to detect in the data available to us...

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I'd be very cautious about saying "CBT is not effective for lessening mental health symptoms" due to a single study. From the American Psychological Association [1]:

> Cognitive behavioral therapy (CBT) is a form of psychological treatment that has been demonstrated to be effective for a range of problems including depression, anxiety disorders, alcohol and drug use problems, marital problems, eating disorders, and severe mental illness. Numerous research studies suggest that CBT leads to significant improvement in functioning and quality of life. In many studies, CBT has been demonstrated to be as effective as, or more effective than, other forms of psychological therapy or psychiatric medications.

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From the NHS [2]:

> Cognitive behavioural therapy (CBT) can be as effective as medicine in treating some mental health problems, but it may not be successful or suitable for everyone.

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From the Cleveland Clinic [3]:

> Cognitive behavioral therapy (CBT) is a structured, goal-oriented type of psychotherapy (talk therapy). Mental health professionals, including psychologists, therapists and counselors, use it to treat or manage mental health conditions and emotional concerns. It’s one of the most common and best-studied forms of psychotherapy.

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I'm not at all suggesting that we blindly trust those organizations, rather just cautioning saying it is no more effective than a pill placebo due to one study.

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A different study that reviewed meta-analyses came to quite a different conclusion [4]:

> In our review of meta-analyses, CBT tailored to children showed robust support for treating internalizing disorders, with benefits outweighing pharmacological approaches in mood and anxiety symptoms. The evidence was more mixed for externalizing disorders, chronic pain, or problems following abuse. Moreover, there remains a need for a greater number of high-quality trials in demographically diverse samples. Similarly, CBT was moderately efficacious for the treatment of emotional symptoms in the elderly, but no conclusions about long-term outcomes of CBT or combination therapies consisting of CBT, and medication could be made.

>

> Finally, our review identified 11 studies that compared response rates between CBT and other treatments or control conditions. In 7 of these reviews, CBT showed higher response rates than the comparison conditions, and in only one review (Leichsenring & Leibig, 2003), which was conducted by authors with a psychodynamic orientation, reported that CBT had lower response rates than comparison treatments.

>

> In sum, our review of meta-analytic studies examining the efficacy of CBT demonstrated that this treatment has been used for a wide range of psychological problems. In general, the evidence-base of CBT is very strong, and especially for treating anxiety disorders. However, despite the enormous literature base, there is still a clear need for high-quality studies examining the efficacy of CBT. Furthermore, the efficacy of CBT is questionable for some problems, which suggests that further improvements in CBT strategies are still needed. In addition, many of the meta-analytic studies included studies with small sample sizes or inadequate control groups. Moreover, except for children and elderly populations, no meta-analytic studies of CBT have been reported on particular subgroups, such as ethnic minorities and low income samples.

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> Despite these weaknesses in some areas, it is clear that the evidence-base of CBT is enormous. Given the high cost-effectiveness of the intervention, it is surprising that many countries, including many developed nations, have not yet adopted CBT as the first-line intervention for mental disorders. A notable exception is the Improving Access to Psychological Therapies initiative by the National Health Commissioning in the United Kingdom (Rachman & Wilson, 2008). We believe that it is time that others follow suit.

1. https://www.apa.org/ptsd-guideline/patients-and-families/cog...

2. https://www.nhs.uk/mental-health/talking-therapies-medicine-...

3. https://my.clevelandclinic.org/health/treatments/21208-cogni...

4. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3584580/

edit: formatting