I would like to help you with your question.
I can understand your concern! Your internal radar went off about what you saw...and you need to trust that radar!
Schools have very strict rules about touching students...hugs can only be shoulder hugs for example. The tutor needs to abide by these same rules.
While certainly this all could be very innocent...and quite normal for the situation...the issue is that you are uncomfortable...and your discomfort must be recognized and responded to.
I do think you have every right to talk to the tutor about this. And...I do believe that you can talk about it in a way that is respectful and appropriate.
You also raise very strong points here about your grandson and the fact that he does not have a father so that any male attention gets magnified.
I think that is the way to approach this with the tutor. Let me give you some possible words to you.
George, I want you to know how much I appreciate the wonderful job you are doing tutoring my grandson. He is doing so much better because of the time he spends with you. He seems more interested in learning (you get my drift here).
As you know, my grandson does not have a lot of male influence in his life. And...certainly...you have become one of the men in his life that he looks up to and enjoys being with. Sometimes, he is a bit needy and I have worked hard to recognize this and to ensure that he gets lots of love and attention from our family and relatives.
The other day when we were at the library, I felt a bit uncomfortable and I would like to talk to you about this. When (grandson) and you were looking at your IPad you had your arm around his waist and also were patting him on the head and back. This amount of touch concerned me. As I said, (grandson) can be needy at times and I want him to understand appropriate boundaries between himself and other people. I know that in schools and other settings, teachers are very limited in their personal interactions with students. I don't want (grandson) to feel confused about the rules at school about touching and what happens with you.
Thank you - I think that this is a very good starting point for a discussion with George. I appreciate your insight.
What I have done here is to provide a clear rationale for the change you want. The focus is all about your grandson...what is best for him...rather than blaming the tutor or suggesting that he has done something wrong. Still...what you are requesting is a strict adherence to boundaries. And...that is precisely what needs to occur.