The landing page is a static background image and I created a clickable area with image map. The problem is that a blue border (see image below) shows up when you click on the a
That's looks like the focus state.
You can avoid that defining
*:focus { outline: none; }
but on the other hand, the visible focus is important for people who don't use a mouse or touchpad, i.e. who only use the keyboard for moving around at a page (keyword ACCESSIBILITY), so you should really consider leaving it as is (maybe only change the outline color to fit better in your page)
That looks like the object's outline.
If you specify outline: none in the CSS for an object, it removes the blue glow that you see when an element is selected in the browser.