Perhaps run this calculator expression on field Shape of your target:

    def getSegment(ID):
     f = arcpy.AddFieldDelimiters("HULLS","LABEL")
     q="%s='%s'" %(f,ID)
     with arcpy.da.SearchCursor("HULLS", 'Shape@',q) as cursor:
      for row in cursor:  pair=row[0]
     with arcpy.da.SearchCursor("TARGET", 'Shape@',q) as cursor:
      for row in cursor:  shp=row[0]
     m=shp.difference (pair)
     return m
    #---------------
    getSegment( !Label! )

BEFORE:

[![enter image description here][1]][1]

AFTER:

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/0BHux.png
  [2]: https://i.sstatic.net/fm4Ri.png