"It is worth mentioning that GABA has long been thought to be unable to cross the blood–brain barrier (BBB) (Kuriyama and Sze, 1971; Roberts, 1974), which raises questions about the mechanisms of action behind its health benefits. However, there are various accounts regarding GABA's BBB permeability. While some researchers argue that only small amounts of GABA cross the BBB (Knudsen et al., 1988; Bassett et al., 1990), with the discovery of GABA-transporter systems in the brain (i.e., passing of solutes by transcytosis, carrier-mediated transport, or simple diffusion of hydrophobic substances), others believe that the substantial amounts of GABA could cross the BBB (Takanaga et al., 2001; Al-Sarraf, 2002; Shyamaladevi et al., 2002). Additionally, as GABA is also present in the enteric nervous system, it has been considered that GABA may act on the peripheral nervous system through the gut-brain axis (Cryan and Dinan, 2012)."

Also, whilst this research largely draws from animal studies, they did also do meta analysis and found the following:

"Assessment of GABA concentrations in the brain using MRS requires a careful experimental design, since GABA is not only present in the brain, but also in blood vessels located outside of the BBB. Tissue fraction analyses estimating blood, CSF, gray matter and white matter presence within each volume of interest should therefore be incorporated (Draper et al., 2014).

Interestingly, evidence has been found for the presence of a GABA-transporter in the BBB (Takanaga et al., 2001). The expression of such a transporter indicates that GABA can enter and/or exit the brain through facilitated transport. In mice, the brain efflux rate for GABA was found to be 17 times higher than the influx rate (Kakee et al., 2001). This complicates the interpretation of GABA concentrations in the brain, and it is possible that this may have led to an underestimation of the extent to which GABA is able to cross the BBB. That is, some studies may have found little evidence for GABA’s BBB permeability because of the high efflux rate."