I am a firm believer that imperfections make the piece. In this case, its really up to you.
I'd probably remove it, as it distracts from the girl in the image. But it also works quite well drawing the eye away and making the girl somewhat 'part of the scene' or 'background' of the image. Take it, or leave it. I do not think it hurts the image, and its removal may or may not help it.
Either way, I'm totally jealous at your models. Most of the people I know are camera-shy.
I have a tips about camera shy people. Before you take someone to a photo shoot, test your model. Ask her for crazy things you will actually not do. I do that to see if they are scared of the camera. if she says yes several times then take her out for a shoot. but be warned some people are shy anyway and its normal so if you still want to work with them do something else, not every subjects are for everyone. never ever force a model, never. both the photographer and the model need to feel good.
During the session just be calm, stay cool, try to relax your model. Make jokes (I like that), respect your model, try to give precise orders.
I tried to be a model once for more than 6 hours I even tried naked pics, its very weird at the beginning to be in front of the camera (why am I here?!) but it helped me understand what they think and feel. If I had to do it again I would it was definitely feeling good
When you model you really don t know what you should do, really. When you get orders and support, like smiles and "you are doing great" you stop think and start relax. some models who are confortable already tend to always do the same "positions or faces" its easier for the photographer but its dangerous. always take care about what she is doing. She may find a confortable expression that will never work with what you want to create.
Also if you are stressed your model should not see it. but after hundreds and hundreds of photo shoot, really I don t care anymore ^^
Either way I like when they are who they are, their style I can't afford paying pro. I just take everyday girls. Maybe one day, I will love to !