There's more than one type of strainer...some may just have a screw in the middle, but others may actually thread into the shoe below. They make a special tool to remove that type of strainer, but on one that has been in there for half a century, there's no guarantee it will come out without breaking something, either it, or something down below you can't see. Then, you may find that the threads on a new one may not fit the shoe below. ANy time you disturb plumbing fixtures that old, you risk something finally giving way. As a renter, you'd entail huge risks if you tried this yourself and then created a leak - BIG liability. You probably won't get the super to replace it unless it breaks.