BobVila.com

I might not understand your problem from what you described, but it sounds like you have wallpaper, not drywall tape, coming loose. Drywall tape should be embedded inside the wallboard joints under a 1/8 inch or so of drywall joint compound, not on the exterior. Someone might have painted over old wallpaper, which is now coming loose and taking the paint with it.

If not, if the tape is just tape and not inside corner-bead, then you probably will not be able to remove it without tearing into the wall. If it is inside-corner-bead, then you can get a piece of the metal and rip it out and re-do it.

If you just have drywall tape, I would sand the corner down below the paint (better adhesion), re-tape it with fiberglass mesh tape (stronger), then smooth a coat of drywall mud (joint compound) over that. You might get a bulky corner, but it is a closet and will be a sound repair.