I don't see how 'let' has anything to do with this example. It is obvious the individual is friends with that other person yet, sorry to say it, doesn't wish to be friends with you. The fact she seems to be repeatedly telling you - and getting short tempered about it - tells me you are ignoring her wishes to be left alone. I think you need to respect her wishes. It is unfortunate you two can't get along and that you can't be on better terms but she has the right to choose not to do so. Hate this all you like but these are the things we must put up with all the time. You need to honour her request to not bother her. Besides, if she is acting in such fashion she isn't really worth your attention anyway.