In Grocery King, the process of clearing all crossed items is called as Checkout. The advantage of checking out instead of just removing crossed items is that you can an opportunity to save your shopping in the history as a single unit. Also with checking out you get the option to save your store receipt and the receipt barcode.
To checkout, tap on the big round shopping cart icon at the bottom center of the shopping list screen as shown below. Note that once items are checked out, the items move into the history screen.