The flywire is part of the Nike Pro combat Uniform, it's not going anywhere as it's part of the construction to strengthen the material.
http://grfx.cstv.com/photos/schools/clem/sports/m-footbl/auto_pdf/new_nike_uniform.pdf" onclick="window.open(this.href);return false;
LIGHTWEIGHT, DURABLE
Engineered high-tenacity yarn
inspired by Nike Flywire is
incorporated into the high
impact shoulder area for
lightweight durability.
I only know this because I hate it as well and thought it was stupid until I read the reasoning behind it which I'm fine with. I just wish they had made it the same color, Brown on Brown, white on white etc something so it's not so noticeable.