Banded Maille is a fake term created by curators of the British Museum. Anyone who has made, worn, or been around maille for extended periods has noticed that when one crumples the maille, small tubes are made out of the rows of rings. They theorized that some armorers would put long strips of leather through these tubes, thus making the maille thicker, and probably stronger.
However, recently some experts with the Historical Armed Combat Association (now called the Association for Renaissance Martial Arts ) have altered suits of maille in this way to play devil's advocate for the curators. However there were problems, as predicted:
1.)Since you have to crumple the maille to put the strips in, this decreases the surface area of the maille by half.
2.)Doing so also doubles the weight since one would have to make twice the maille for the same surface area.
3.)For all the added negatives, little is improved. It did make the maille structurally tougher, but had the same degree of weakness to piercing attacks, which was what did normal maille in.