A product can be marked as purchased either with a tap or with a left to right swipe gesture. Select either of these ways in the application settings.
According to the selected method either tap a product to mark it as bought or swipe it left to right:
The product, that you've just marked as purchased, is shifted to the beginning of the bottom part until you close or minimize the app. The other crossed-out products are sorted either alphabetically or by time depending on the way of sorting selected in the app settings.