If by "checkout" screen you mean the "Review items and shipping" where the yellow "Place your order" button exists to actually "order" the items, then "delete" is hiding behind the "Qty" dropdown that is present on each item (at least for me). You have to click the "Qty 1" dropdown, and only then does the "delete" option appear.

So it is well hidden away, but at least for my Amazon account, one can delete from the "checkout" screen.