Thanks Rollin and Muddin,
I applied some white grease and here's what happened.
I tried and tried to insert this "cone-shaped grommet" without luck, and I walked away (ran out of descriptive words) and had supper.
I went back to it and resumed squeezing, pushing, etc.. and all at once the middle of the (coned-shaped grommet) fell out and the two pieces looked like a plug and a regular doughnut grommet. The doughnut grommet went on and plug went in a minute, and all is right.
Seriously, apparently some mud / grit stuck the plug to the grommet and the whole thing came off, and the grease did it's job!