GXP has almost no connection to Tenchi. The director admitted to having minimal knowledge of the series and pretty much doing his own thing. No original Tenchi characters even appear in it, though there are a number of relations, like Mihoshi's mom.
PS - Tenchi Universe is not a retelling of the OAV. The story is completely different except for the same vague premise.
PPS - The 3rd OAV series has started. 2nd ep came out in Japan just recently, though I haven't seen any of them.
"I've watched while the maggots have defiled the earth. They have
built their castles and had their wars. I cannot stand by idly any longer." - Otogi 2
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