how to add a remove coupon button to commerce checkout page
I was not able to recreate your issue. 'Remove' button was available next to the applied coupon.



The version of coupon code, I'm using is 7.x-2.0-rc2.

The steps I took were:


Added a discount and associated a coupon code with it.
Added an item to cart and checked out.
After confirming checkout was given option to add coupon code.


Checkout settings:


Note:


  The problem could be with checkout page. You can use order_coupon_list
  view block below the coupon code apply form.