My brother has an Ibanez with this bridge (I can't find a name or model without taking the back off):

The highlighted piece is missing for the high E string. What is that thing called (a vice?), and where can I get a replacement or replacement set without buying a whole new bridge?

Or, better yet, what's a quick fix?
Oh man, the technical term for it escapes me. I think it's called a lock block or something to that effect. Ibanez sells parts direct, and some dealers may have them. that is an Edge III trem btw. You can use it without the block, but you need to leave the ball in on and you can't really use the trem.