False Internet Death Threat Claims

Someone online is threatening to report me to the cops claiming I made death threats against them on an app and I'm wondering if I should even be worried. The app is Yikyak, this person and I don't like each other, they posted a real photo of themselves online and I told them that somebody could find them and hurt them so they should take it down. They are now insisting that it is a death threat even though I flat out said it wasn't afterward and blocked them. Sorry if this is a dumb question but I'm kind of young and I don't really know how serious this is