This piece has been missing since we moved in. Bought one from Home Depot and part that screws in was way too big. Does anyone know what kind I would need? When I went back to Home Depot, it looked like the only thing that might fit this is a drain strainer, but I would rather have a pop up stopper. 
Add a pop up drain stopper to this bathtub
bathtub
Related Solutions
The drain will unscrew... you might need a drain key (or expanding tub drain remover). Here's a video: https://www.youtube.com/watch?v=T_0vYme1Q88
Or you might be able to grab it with a pair of channel locks:
But if you don't care about it any more then you could use a dremel tool to cut a notch in it so that you can use a flat head screwdriver and a hammer to unscrew it.
You also find drain assemblies with 1-1/4" tailpieces, but they're almost exclusively used for sinks. They're used with a 1-1/2" to 1-1-/4" reducer since the PVC drain plumbing usually won't be smaller than 1-1/2".
The diameter of the actual threaded drain assembly isn't smaller in these cases. They fit the sink/tub the same way. Just the tailpiece is smaller.
Post photos of your situation for more specific advice.
Best Answer
You can replace the silver drain spud ( the silver part in your tub ) by using this special tool. You can replace it with one that will accept the stopper you have or any other.
You place the tool into the spud and use a crescent wrench or a screw driver thru the hole to gently turn it counter clockwise to unscrew it from the drain pipe under the tub, then install the new one in the reverse.
Use a little lube on the new treads and some plumbers putty under the flange when you put the new one in. There is a gasket under the tub between the drain pipe and the bottom of the tub, this should stay in place but be careful not to let it fall down inside the space under the tub.