The table you auto-create for the cart has a complete header / section that says:
<th class="eC_FormItem desktop_only">Remove</th>
So I was (naturally??!!!) expecting something to show up there in the relevant <td></td> sections in the table, which stubbornly remained blank!!!
I did not even think to look where you say it is, and that I now see it!!
I can style and place it more appropriately now I have observed it.
My fault, sorry.
And thank you so much for everything else.