How to get the ternence spout out with the given tool?

I managed to get the spout in correctly no problem with the directions given here on this subreddit using the supplied installation/storage tool, but that tool is too wide to push the spout back past the ring so that you can easily flip the retainer ring and pull it out.

Don't worry btw, I managed to get it out by basically futzing around through my skin but it was painful to say the least.