I have a Grizzly lathe and just purchased a drill chuck and new
arbor. Now I can not get the rotating bearing tip arbor out
of the tail piece as if I pry on the bearing I am afraid of damaging
the bearing. Any suggestions.

Nip

Ignor the arbor problem as found the problem--now I feel stupid
but you can't make a mistake if you do nothing

Don't feel stupid! That's how you learn.