I got "back to top" link under each item.

1.

I was able to do this by making a copy of the default folder under /components/com_k2/templates
I called the copy "custom"

Then open the k2.php file in an editor and go to the bottom of the file.
The Back to Top link starts at the line < div > I deleted the entire div block to remove the link.
The final step is to edit the K2 menu item (if you have one with multiple categories) or the categories that you want this removed and change the template from default to custom.

2.

It can also use CSS to hide the DIV-block, with     /components/com_k2/css/k2.css    .itemBackToTop{ display:none }