How is this type of weather stripping replaced?
I have seen this type of weather stripping many times on sliding doors.  There is a flange on the weather stripping that fits into the mill work.  It is a bit difficult to remove, and even harder to replace.  They sell the replacements at most box stores.  It is important to remove the flange from a small dido (gap) in the frame. Putting the new one in is tedious and often frustrating, but can be done. It is truly a poor design.  Take your time, use a little wood glue as lube and a way to keep it in place, or use a surface mounted replacement. I have had some  success with self adhesive  pillow type weather stripping.  I feel your pain!  lol.