Those blinds are super easy to replace and much cheaper than any deposit. The Landloard (or the toady and furtive maintenance man) have likely sourced those from the closest (or the second or third closest if it's cheaper) hardware store.
If you study the mounting of the existing blinds. It's probably pretty easy to buy a similar replacement so you won't even have to install the mounting hardware. Your cat didn't damage that.
the big box store can often cut blinds to fit your windows if they're not standard size.