Mirror Splashback in Kitchen

Hi, We had a mirror splashback installed when we did our kitchen renovation 2 years ago. I clean it every night when I do the dishes with fresh hot soapy water and a microfibre cloth and I then dry it off with a flannelette nappy. It has always come up spotless but I have noticed recently that there are marks that I can't get off - mainly behind the burner that we use all the time. Anyone else had this problem? Does anyone have any suggestions on what I could use in the hope of removing them. I think it is probably oil stains... Thanks in advance.

Have u tried water & vinegar in a spray bottle?