Hello Itzel. I don't really see a problem with putting your previous work experience. Your possible employers wouldn't go out of their way to get you in trouble for it. I have had a variety of jobs ranging from hostess, office assistant, retail, and the list goes on and on, and have always put my experience and even made it up in some occasions or exaggerated it. I think a few times they did care for experience, but not in general. Getting a customer service job in the end boils down to how you present yourself in the interview. By experience watching my bosses discussing whether to hire an applicant I heard them asking if the person seem happy/smiley/peppy enough. It seems ridiculous, but they just wanted someone that can keep a smile plastered on their face the hole day.
So my advice is to not be afraid to put your previous experience if you have any.
If you can't shake the worry of getting into trouble and don't want to put it anyways, it still shouldn't be a problem.