Same exact thing happened to me! I thought the glue was under the glass too but that's just a plastic piece attached to the glass and it too needs to come off. So you run your guitar pick UNDER that plastic piece attached to the glass. Then u just clean the glass & glue off of the digitizer. Being very careful not to put a lot of pressure on it. I finished the job but now I am having issues with digitizer. I may have to take it to another shop and let them fix it right. Then at least I have some recourse. This is a harder fix than it appears!
