And I don't want them to appear.

I disabled all possible borders and now those dots appear when I press the buttons.

Is it possible to remove them?

(Atahualpa 3.6
W.P latest)

You should install Atahualpa 3.6.1 as there were some issues with 3.6. It can be downloaded at wordpress.bytesforall.com. Also can you supply a link to your site?

Sure, I will upgrade (will it override my current setup?), thank you.

It should not affect your styling but you should do a manual upgrade so that if anything is not quite right you can just switch back to your current theme version. And of course backup first. Here are the instructions.

Yes, I did that, everything's ok.

Do you have any idea on dots?

I would first determine what the selectors are for the dots with Firebug in Firefox. It is most likely a dashed border. Then I use border:none or border:none !important with that selector.