This is a very disturbing study.
No dx of original existing GI complaints (how could the authors be sure they were not harming the patients through mistreatment?)
Almost one-third of ASD patients in our sample had at least one fGID. The presence of fGID functional gastrointestinal disorders was associated with ID, sleep problems and with behavioral problems (as measured by the prescription of psychotropic drugs). 
No participant breakdown by sex, race, or intellectual impairment, which I would suggest is useful data.
ID would be useful since so many participants are shown as significantly improved. One source says 30% of those with ASD also have ID.  Another study, from Italy, found about 47%. 
No attempt to ascertain if participants received any other therapy or treatment during the 2 years (other than med changes). These were school age children, under age 10. Surely they were provided some sort of help in, or out, of school?
It is not uncommon for non-verbal autistics to become verbal, and for other “characteristics” to also lessen or disappear. 
The original study methodology suggests that the participants were subjected to uncomfortable, painful procedures to prepare for the fecal transplants. As an autistic adult, I would suggest that the only reason that the oversight group allowed this was that the children involved were unable to communicate their pain, fear, anxiety, etc. They were test animals, not human subjects.
 Penzol MJ, Salazar de Pablo G, Llorente C, Moreno C, Hernández P, Dorado ML and Parellada M (2019) Functional Gastrointestinal Disease in Autism Spectrum Disorder: A Retrospective Descriptive Study in a Clinical Sample. Front. Psychiatry 10:179. doi: 10.3389/fpsyt.2019.00179
 Hervas, A., and P. Romarís. “Functional adaptation and disorders of the autistic spectrum.” Medicina 79 (2019): 10-15.
 Postorino, Valentina, et al. “Intellectual disability in autism spectrum disorder: investigation of prevalence in an Italian sample of children and adolescents.” Research in developmental disabilities 48 (2016): 193-201.
 Helt, M., Kelley, E., Kinsbourne, M. et al. Neuropsychol Rev (2008) 18: 339. https://doi.org/10.1007/s11065-008-9075-9