My own personal opinion says we should let them keep collecting. I myself feel odd around personal objects, such as glasses and jewelry, although I do so love to see them.
However, the non personal stuff, like plates and wine bottles, I see nothing wrong with bringing up. They belonged to no one in particular, and the only story they hold is the one from when they were made until they were broken.
They also depict more of what a cruise on the ship was like, rather than personal objects that show what life in general was like.... which, I think someone already said, we already know about from books.


Now, business wise, I don't think a petition will do anything. Beucase, if you read the same website you got your expedition facts from, they state very clearly how much they care for these objects and how well they treat them. So, I think in their minds, salvaing is fine, as long as they take extreme care with the objects.
I think if you send them a petition they're just going to write back saying how much care they taken in bringing the objects up, and how much they want to preserve the memory of the passengers on the Titanic.
(Also, I think on the site it says they have stopped bringing things up, since the wreck is to fragile to navigate)

But, good luck in your efforts!