I guess you've never bought touch-screen-compatible gloves… they are the norm now, even cheap gloves from a dollar-store as well as higher end ones. It needs to have material that is conductive.
Don't even need those, screens work alright with cheap/thin gloves.
"Furiously" probably because the touch input is not as reliable, but it does work. Modern touchscreens are quite good, I was surprised at how well the work through various fabric.
Because being returned your phone with the fingerprints of a police on it as a bonus, could backfire in a spectacular way for the agent