I may be wrong but on most fridges the filter like material on top of them is actually insulation between the fridge and the cupboard/bench/wall and is to keep the heat and hot air away, yes insulation will just crumble when washed usually, there should be a baffle made of metal or timber between the rearof the fridge and the insulation on top to direct the air out the top vent.
To replace it just use a bit of a roofing bat, stick your head into the roof cavity at home and just grab a chunk to use.