Obviously a little part of the texture's lips is painted onto polygons that don't belong to the lips material. Judging by your picture you seem to have the tools to edit the texture itself, simply open the texture in Photoshop load the uv template on another layer set to multiply to see only the polygon lines, and with the clone tool simply paint out the area that is not on the lip polygons. Remapping the figure may not do it especially if the textures problem area does not fall precisely on polygon border lines.

Dominique Digital Cats Media