There are a couple different kinds of push pull tub drain stoppers. One is a rubber stopper that isn't attached to the drain, and the other is a metal stopper that is attached to the drain. Removing both of these is a quick and simple procedure, and can enable you to unclog drains and clean the drain area on the tub thoroughly.
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Look at the stopper in your tub drain. If it is a metal stopper, you can try two things to remove it. Some push pull stoppers can be unscrewed from the drain. Pull up the stopper by the knob on top, and begin to unscrew it counter clockwise as one large piece. If it can be unscrewed this way, it will come undone within six to seven full circles.
Try a different method if the stopper doesn't come undone with this method. First, unscrew the knob from the top of the stopper counter clockwise. Next, use your fingers or a flat head screwdriver (if there is a screw in the top of the stopper) to unscrew it counter clockwise.
Remove the drain stopper completely and set it aside. To put it back on, just reverse how you took it off, by re-screwing it on clockwise until you feel resistance.
Try a different method if the push and pull drain stopper in your tub isn't metal. If it is a black rubber stopper, this is much easier to remove.
Grab hold of the knob on top of the stopper. Push it into the drain slightly, than pull upwards until it pops out.