My years of experience have prepared me well for this marketing role. You mentioned that customer service is a big part of this job; I spent three years working in a high-volume call center, answering customer calls and identifying solutions.
I developed extensive skills in working with customers, even when they were distressed. I'm excellent at deescalating situations and finding a way to make the customer happy. Our customer satisfaction rating rose 10 percent during my tenure at my previous employer.
Since the role of your marketing department is to improve customers' impressions of the company, my experience will be an asset to your team.