Thankfully, there's an easy way to remove those advertisements from Skype and enjoy a clutter free user interface. Here are the steps:
1. With your Skype open, click on Tools and then choose Options to open the Skype Options window.
2. On the Skype Settings window, go to the Notifications tab and then click on the Alerts and Messages sub tab. Remove the check marks on Help and Skype tips and Promotions.
3. Restart Skype to enable the changes you've made and enjoy Skype without advertisements!
Please remember that these advertisements are a source of revenue for Skype. Disabling them removes the chances that Skype may earn from those advertisers.