As is apparent from the fact that we are all having this discussion, the OP English could have been stated more clearly than it was. Still, I think it's very possible to make sense of it. Its logic is based on the fact that the sooner (i.e., earlier) the member books the award-night, the sooner (earlier) the member will get the referenced e-mail.
So, if the member books eight days in advance, the member might get the e-mail just one day before their arrival date. If the member books 15 days in advance, they presumably would (be likely to) get their e-mail seven days before the arrival date. The earliest they will get the e-mail is seven days before.
Maybe I misunderstand Alan's #7, but I don't agree that a number up to seven ends at six. IMO, a number up to seven includes seven.
Also, I disagree with this: "Up to a point in time 7 days prior to an event; i.e., more than a week." Up to seven days would include the seventh day, IMO, but not more than a week.