Pilot bushing, need to replace?
I read somewhere, probably on a forum, for new ones soak them in oil before installing.
I can certainly grease it.
Even if I had a puller for it, I think there is a certain type for that, I'd probably be hesitant to pull it out - if it ain't broke, stuff happens, you know.
Everything is in good shape, so I questioned it. I'll certainly take another look, or two, or ten.