What tool do I need to take the bottom part of the toe touch drain?

Which one is yours? Back to you, Tom

If the toe touch strainer has a cross bar inside it once you remove the pop top then you can simply use two screwdrivers crisscrossed across each other and the cross bar to unscrew it. If that doesn't get the strainer out you could purchase a tub drain removal tool at home depot...see image. That should work for you!

If you do not have a cross bar for some reason post back and let us know, OK?

Mark