I don't know the name of the climb, but it was well around the corner (to the right) and uphill - a good 50'+ from the first aid kit. That said, sounds like I may have inadvertently swiped it nonetheless. Will PM details to confirm.
Yeah that rope has been there for quite some time. That route is cuttlefish. I don't actually know whether it serves a real purpose or not, but the WMCC often keeps other communal equipment in that dry sun protected notch so I think that rope belongs to them and is left there on purpose.
There used to be a first aid kit under that route too, but I guess that moved to the left closer to the wall of early morning light.
If I were to hazard a guess I think that's a piece of retired cord that they use when they replace the fixed lines on the upper tier it something like that