Rubber seal or weatherstripping on Odyssey tailgate window?

At the top of the rear (tailgate) window on my 2003 Honda Odyssey, two narrow strips of rubber - apparently seals or weatherstripping - are drooping down from beneath the tailgate frame onto the outside of glass. If I push them back under there, they soon dangle again.

They are about a foot long and rectangular in cross-section, maybe a quarter of an inch wide and the same height. Anybody know what they are, what their function is, and whether I can just pull them all the way out and throw them away?