The reducer is a ring within a ring. It should come out, but may be a little stuck from friction. Put the table in the sun until it's really warm -- it might help loosen things up.

Flip the table over onto some blocks or something that will lift it off the ground (put down a blanket so it doesn't get damaged). Or if you have soft grass, place the table upside down on that. Find a strong object that's bigger than the inside hole, but smaller than the outer ring (look around the garage and house for anything that's the right size but won't break easily. It could even be a smooth rock.) Place it against the underside of the ring and tap it with a hammer until it comes out. If you can only get it out part way, flip the table again and see if you can grab the reducer with some pliers and pull it out.

If you don't have the right size object to use to tap it out, go to a hardware store and look for a dowel or short piece of pipe that's the right width. That will only cost a few dollars.

I cannot thank you enough for providing such detailed instruction. I am trying to figure out if the reducer was already taken out or if indeed it is still in there. You sound so knowledgable. I am attaching a pdf with the parts. I wonder if I could remove it without having to flip the table.

OMG thank you! I figured it out. WD40 and punch it from underneath. THANK YOU!