It holds the hook pretty snug to the rack. One end goes through the eyelet of the hook and the other end around the rack. They make different sizes so make sure the ones you get will fit around the rack.

I've never had issues with these panniers coming off. I think every time they've come off is because I kicked them.

NiteIze makes a ton of carabiners, S-hooks etc so check out their website or REI. Depending on where you live, Fred Meyer has a large selection of them too. The package opens without tearing so easily returned if they don't work.

Edit: I see you're in Michigan. Fred Meyer is probably known by it's parent company Kroger out there I assume.