How to replace a Gerber Toe-push tub drain stopper?
Take another look at PF waterworks TubSTRAIN Universal Toe Touch (Tip Toe or Foot Actu.) that is referenced in the question.



Per the image the TubStrain product has a #10-20 fitting included.



On the back of the package the adapter is referenced as “F”



Another issue to take note is the Gasket. If the gasket placed the wrong way the Toe Touch will not work. Make sure the larger diameter of the gasket is pointed toward the drain and the smaller diameter is pointed towards the silver cap. Like an umbrella.



Also sometimes the gasket doesn't work, because they are smaller than the drain opening. Danco sells the gasket only. Replace the PF waterworks gasket with the Danco Rubber Tub Drain Gasket.  



Rubber Tub Drain Gasket in Black