I have found 2 papers that may be relevant to your question -
This paper probably answers your question the most - I have only schemed through it, and it seems that the results were insignificant. You can check out the paper in more detail, hopefully it will get you to more resources that can help with your research.
I have also found this paper which ...
TL;DR: Multiple approaches have been tried over many years. Current medical evidence strongly supports an "affirming approach" to alleviate gender dysphoria. "Corrective approaches" are considered unethical, and withholding treatment is not considered neutral. It's explained in the referenced AAP slides, e.g.:
Children rejected and not supported are at ...
Interestingly, the authors appear to have been aware of your concern:
Given that the only difference between these groups involved a subject
variable for which there could be preexisting differences in DTA, we
included a third group of creationists who read a nonthreatening
Since the evolutionist/anti-creation and creationist/control groups ...