Hey thobias -
All you need to do is go back to the original file before running the Unmasked Alpha action (hopefully you saved it in Photoshop like Mr. Kladis suggests) and take your alpha and cheat it inward by 1 to 2 pixels. This will get rid of most if not all of the lines. I marked on your TGA where I am getting this information you can see if you turn the Alpha channel on in Photoshop that the places you are seeing lines are also the places where the alpha doesn’t do into the sprite enough.
Thank You
Eric Ketchum