Welcome to the forums TMonroe. First off you should know that just because you Google an image using the term free it does not mean the image is free. Copyright exists from the moment a picture is taken and it does not need to have a watermark or copyright notice on it to show that it is copyrighted. You may wish to reevaluate any other images on your site or sites that you have obtained this way.
Unless you take the image(s) yourself or hire a photographer with a contract that says you obtain all rights to the images you purchase you can never be completely sure nowadays. As in my case I obtained my image from a personal website where the owner of the site had several image galleries including one labeled for the public in which all the images in that gallery had his name on them along with a title he gave them. When I selected the image I felt very confident it belonged to him and he was offering it in his public gallery, so you see why I make the statement that I do.
Now having said that, yes absolutely I would request proof of Getty's claim and their exclusive rights if they have claimed them in their demand letter. I would not mention anything about the Google search or no watermark for the reasons I have stated. Read the forums and educate yourself as all the answers you need to defend yourself are contained within. Please keep us posted as to your progress.