Strange stopper in bathtub drain

I have a small chrome rod sticking out of my bathtub drain. I'm trying to put a strainer into the tub but this rod sticks out. Does anyone know what it is? How to remove it or better yet is there some kind of strainer to put on it? It seems to have a small nipple but no threads. Any ideas would be appreciated.

Not really that strange at all, is there a lever on the overflow trim?

So what can I attach to it? The overflow trim is sealed-off; no lever. You think I can just push it down?

That would normally just unscrew from the tub drain. It is the "remnants" of a push/pull stopper. Otherwise, just remove the entire drain piece and install a replacement one.