Taking down ivy

I've just taken down an ivy and it's left loads of it's clingy bits to the wall. I've tried using a wire brush to remove them but that is bringing of the rendering as well. Any ideas on how to remove the leftovers?

 

If you have cut it off at the base the 'clingy bits' will eventually die and fall off, but that will take some while.

Have you got rid of the whole plant, ie. dug the roots out aswell? Ivy is very difficult to irradicate, as any small pieces of root left in the ground will re-establish. It will need to be poisoned, to kill off the roots.