Well, GTE is basically green tea leaves in supplement form. L-theanine is a standalone ingredient. A green tea extract-extract if you like.
It looks like L-theanine is in the clear though.
Mechanism of Injury
Preclinical and human data implicate the catechin component of green tea as the culprit of hepatotoxicity. Approximately 10% of the green tea extract is composed of catechins; of these, epigallocatechin-3-gallate (EGCG) is present in highest concentration. There is great variability in the concentration of green tea extract, EGCG and other components among marketed products, which may explain while some products have been implicated in hepatotoxicity. Exposure of rat hepatocytes to EGCG has been shown to induce mitochondrial toxicity and generation of reactive oxygen species. The association of liver injury with higher doses of green tea (as in extracts) suggests a component of direct hepatotoxicity, perhaps in the context of some degree of host susceptibility exacerbated by environmental features such as obesity, fasting or glutathionine depletion.
That link also says
Liver injury typically arises within 3 months, with latency to onset of symptoms ranging from 10 days to 7 months
I've been using l-theanine for years.