On some toilets, the flapper valve sometimes comes with a float. Others here have indicated that they sometimes have become detached, and end up clogging the siphon jet once flushed down. You may have to end up trying to push it back out. Trying to grab it at the jet's outlet, as you've found, it probably nearly impossible.
If you emptied the water, and then took something like a coathanger wire, you might be able to fashion a hook on it, and pull it out or push it back. That would be a stretch, though. What might work would be to heat the end with a torch, then, try to push it into the thing, once it cooled, it might then become attached enough to pull it out, or maybe at least hold it where you could try to cut it up some so it was small enough to get out. Don't think there are likely to be any chemicals you could put in there to dissolve it, at least none that wouldn't risk problems with the plumbing.
Good luck, and let us know if you solve it, and how. Maybe someone else will have a better idea(s)...here's hoping.