windshield glass...caulk necessary?

The person who installed my windshield glass put black caulk on the edge of the rubber seal. He laid a bead of sealant/caulk where the rubber seal meets the glass, inside and outside. Well, now the caulk is peeling off and I'm wondering if it's necessary...and if I should remove and put a new bead.

It has only been on for a year. if I need to replace it, what type of sealant/caulk should I use? Is there something that wont peel like what was there?

 

damn that was fast...

yeah, the gasket was brand new and so was the glass...I guess the guy put it on for extra measure. Thanks, I'll peel it off....or let it peel off completely on its own