I'm currently in Cyprus and they were offering me tea with the word chai as we all know it comes from Chinese word 茶. But since the Greek must have been using herbal infusions for a long time. The word tisane, πτισάνη, came up with some DDGing. http://www.infusionlink.com/infusions/tisane/ But the Cypriots I asked about it didn't recognise it.
This probably won't help in your specifc situation, but the ancient word was enchyma. There may be also a word related to the verb brechō. These are more words for a medical infusion, or the act of infusing, rather than tea as a drink for pleasure.