I would "trim the edge" with a razor blade, and then novus#2 it 5 times. It takes practice and is the much quicker DIY approach. The playfield coats on an IJ are fairly thick. Just make sure the blade doesn't touch the playfield! Don't cut the way your normally would through the material, hold the blade edge flat to the play filed to make a trim. I wouldn't do this to a CQ or a "museum piece" IJ but if it's just a "player", that's what I would do.
If you really do try this, make sure you practice on something else. All you really want to do is remove 1/16 of an inch at the black dirty part. Mylar tears/cuts kind of like strong packing tape. Knowing that helps.
Looking at your mylar again, I would make a cut from top Willie black key line to the bottom Willie black key line to remove the lifted/dirty spot.
(Mylar gets dirty spots because over time, the edges lift away from the play filed and dirt floats under it.)
Alternatively, you could completely clean out the black dirty part with the edge of a small rag and some novus #2, then just trim off the small, unattached sliver of mylar. That would be the safer and quicker approach.
Novus it a bunch using moderate pressure along the edge of the mylar cut and it it should become very smooth and clean if you use novus. You can really make old mylar look very good with novus2, just don't go crazy with it.
If you want to remove the entire piece, see my tips below.