What I would do :
1remove beading arround glass and paint the beading same colour like a door.
2. Remove glass and clean from paint with Stanley or any cheap blade..
3 put back glass and bead
4 put tape arround beading if you can go under the beading if not enough space then put the tape as close as you can to the wooden beading.
5.i would repaint the all door possible..
6. After 48h with the new blade cut all along the tape next to beading then remove the tape gently.
You should be satisfied with the effort and work and Finish now..
I hope I could helped..