After signing in to the status page, click on "my recommendations." If your letters have been received, there will be a large green circle with "ok" inside it to the right of each letter. The headings for each letter will also change from "Recommendation 1:" to "Recommendation 1:has been received!"
I mailed my letters 8/15, submitted my app on 10/3, and was complete 10/3.
They will update the status page, but it seemed to take awhile for the website to register this. I think every other school I had applied emailed me to say they received my LORs weeks before Duke updated my page.