How can I remove this flapper alternative?
This is what your flush valve looks like, when it's not in your toilet.



This bit should be flexible enough, to allow you to bend it out of the way on both sides.  



The pins holding the actuating unit in place should slip out of the holes, and the whole piece can be removed. The best method to remove the actuating unit, is to gently pry the bracket with a screw driver on one side, then twist the actuating unit so that the pin on that side pops free.  Once one pin is out, it should be easy to get the other side out.