Despite the fact that the Jurai prevents any unoffical contact with the people of Earth, some things from Earth have already appear in the galaxy. The most noticable items from Earth are carrots and popcorn. Noike is able to notice carrots. She was amazed at finding the planet where carrots have come from. In GXP, Seina and Urma(Ryoko) were eating popcorn.

I think that the Galactic Union is already aware of the planet Earth. It is likely that the Union sees Earth as an oddity. Lately, some worlds are starting to notice some of the strange events are occurring on Earth. The events related to Tenchi.

You make a good point...

Well, you assume that carrots originated on Earth. But when Masaki-Masaki came to Earth 150,000 years ago, she may have introducted various crops to Earth at that time.

Now imports from Earth to the galaxy is possible. Given what we saw in GXP with 'Washuu" running as shop in the GA, she got her goods somewhere. Still, remember that Earth's existance is still a highly classified secret according to Kiriko. Therefore how much open export would be allow from Earth?

The Galactic Union is aware of the planet Earth. I think that the Galactic Union sees Earth as an oddity. The Earth is located in Jurain terroritory. Earth has been place in a special protectorate zone.

Katsuhito informed Tenchi that many members of the Masaki Family enter space after they come of age. In Japan, the legal age to become an adult is twenty. It is likely that the Masaki Family considers 18 to be the coming of age.

The events involving Tenchi and company are considered classliflied as Kiriko told Seina in GXP. The De Luma Guild was not aware of Tenchi and company when they had tried to take the Seina's family hostage.