Nope, it's definitely not "I was wondering if you'd like to join Gaia and I for some tea" any more than it would be "I was wondering if you'd like to join I for some tea", though it's a common error.

To clarify the sentence's subjects/objects for RuriStone and anyone else wondering: The subject of "was wondering" is "I" (Ryne, doing the wondering), and everything from "if" on is the complex phrase that serves as its object (that which was being wondered). The subject of that phrase's verb "you'd like" is "you" (the player, doing the wondering), and its object is the phrase that follows it (what's being liked). The subject of "to join" is still "you" (the player, doing the joining), and its object is "Gaia and I" (the ones being joined).

Here are a few references:
https://www.britannica.com/dictionar...-Use-Me-and-I-
https://www.grammarly.com/blog/grammar/me-vs-i/
https://www.grammarbook.com/blog/pro...-vs-me-review/
https://www.bbc.co.uk/worldservice/l...rnitv264.shtml