weather stripping for commercial door

Hi--I have a business with an old metal/glass door. The building owner seems to have scotch taped this felt weather stripping in the channel. It doesn't work well, and in the winter, my double keyed cylinder lock freezes up, and it's difficult to get in. Not sure how old the door is, but I would guess at least 30 years (probably more!)

It looks like the channel flares into a triangle shape as it goes inward toward the door itself. The depth and width of the channel are 1/4". However, that width is measured where the channel is flush with the side of the door. As I said, it appears to flare inward, making the actual width inside the metal casing of the door a little larger.

Not sure what the best thing to do is, here. Thanks for any advice you can provide.