We have heard that some customers have had problems removing broken toe sliders and tongues - this only applies to bindings that come with the "hinge" EST baseplates. Bindings such as Diode, Genesis, Cartel or Escapade.
Since there is a stud connecting the two parts of the baseplate there is not too much extra space for sliders and tongues. For that reason it takes some sensitivity.
Try using some pliers so that you have a better grip on the plastic and push the strap from top to bottom by wiggling it forward and backwards. With this technique it can be removed within seconds.