Try rigth click and in the quad menu "unfreeze all"... maybe its freezed and you cant select it...or maybe its something else like a sight line from a camera or ligth attached to the model.It is grouped?... try selecting and "group"-> "open" so you can edit or delete individual elements (if it is a group also).Try a wireframe view so we can better see where that line land inside your model.
No worries i think all of us have been there. (myself included). I was out of gizmo for 3 days cause never know the proper name to look for in google (i'm spanish speaker, i learn english throug this forums like this).