Sorry to say, but there's a "delete" option for every item on the checkout page. Just click the quantity dropdown and change it to "delete". Simple as.
I don't mind, for whatever reason it wasn't usable for me. And maybe it wasn't there.
Edit: I checked again. It isn't there. Note that I said checkout, not my cart. It has big CTA buttons to go straight to checkout without first going to the cart.
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.
Edit: I checked again. It isn't there. Note that I said checkout, not my cart. It has big CTA buttons to go straight to checkout without first going to the cart.