Can I ignore some website element when navigating using the tab key?

display: none it instead.

You can use tabindex attribute to define order in which the tab key should cycle through elements. If you set tabindex="-1" the element will be skipped.

More info is available here http://www.webcheatsheet.com/HTML/controll_tab_order.php for example.

UPDATE changed tabindex="0" to "-1" based on comments

You can set the tabindex="-1" on this element so it's ignored in the tab order. 0 tells the browser to figure out the tab order on it's own, -1 tells the browser to ignore it.