Agree with rayrick. They make it seem more like an honor than it is. Some adcoms view this kind of trip with skepticism, thinking all it says is that this family has the money to send their kids on these trips. But if it’s something that your dd would enjoy and aligns with her interests and you’ve got the money, then it’s OK to consider it.
My kids did the Duke Talent Search thing, but we couldn’t afford the expensive camps they send you info about. We found a less expensive alternative that gave scholarship money. This was a three-week camp over three summers after their sixth-, seventh- and eighth-grade years. It was a wonderful investment as they learned not just about the subject matter but also what it’s like to live on a college campus, share a room with a stranger, eat in a dinning hall, dealing with a community bathroom, etc. Ds1 even worked there as a counselor one summer in college. But, yeah, just don’t delude yourself into thinking this will provide some kind of competitive advantage for college admissions.