Gratuity was added to the bill. Was I still supposed to tip?

I recently hosted a birthday party at a restaurant where I paid for appetizers and dessert but the guests were responsible for ordering their own meals and drinks and paying for them. For a party of 13 people the entire bill was about $145.00. The total included a gratuity of 20% already added to the check. Everyone came together to pay the bill in cash. Together we handed the waitress $160.00. When she did not mention giving back change or return the table, I asked her for the change and explained 20% gratuity was already added to the bill. She seemed a little upset but provided the change. Since gratuity was already added to the bill, did I display proper etiquette at the restaurant? The service was good but an additional $15.00 seemed a bit much for a tip.