What way is there to make a conspiracy go away? Like destroying it or returning to hand?

There isn't much.

You can use the Cthulhu event 'Dragged into the Deep' to send a conspiracy to the bottom of its owners deck. The neutral support card 'Foiled!' will black a conspiracy text box, which can be quite useful.

If Conspiracies have text boxes then I believe Frozen time can blank them.

P.S.- After checking the rule booklet it seems that Conspiracies/stories do have textboxes.

There aren't many ways. However, this is I think as it should be. If someone has 4 success tokens on a Conspiracy it shouldn't be a commonplace thing for their opponent to be able to erase all of that with one card.

Besides, until Venice it was hard enough to get people to use Conspiracies - don't want to immediately make them seem unplayable again.

Okay, that's what I expected. Thanks!