Since Kongregate updated their ad system, there are now some ads which will require you to open a new site, interact with it and so on. If you have enough of it, all you need is the web console of your browser. For firefox, you can open it with ctrl + shift + k. If you have it open, copy and paste following it into it:

window.ssa_json.onCampaignCompleted(); window.ssa_json.onCampaignClose();

The first line triggers that the ad completed in background, and the second line triggers that you successfully watched it and pressed the X button to claim it. All you need to do is to press that button to get rid of it, but the game will continue in background meanwhile.