How do u remove the oil tube 2 get the oilstick out that broke down inside

The handle broke off right at top. It looks like there is so easy type of hard plastic pushed down on there. Tried to pull out but didn't work. I could send a pic of it tomorrow morning if that will help.the tube looks fine e.

A good drill. Pre drill a small hole smaller than a drywall screw. Screw the drywall screw into the plastic and pull piece out with pliers.