bilbo baggins

Hello, I have an Alvarez cheapy acoustic guitar that got too close to an electric heater a few years ago. The result was that the black plastic binding on the top of the lower bout melted. The big problem (beyond the aestetic) is that the melted plastic binding sticks up and is sharp exactly where my arm rests on the upper bout. I have thought about trying to melt it back into place or replace it, but want to get opinions from people who know what they are doing! Any suggestions? Thanks