Total speculation based solely on experience as a consumer (and I own a 2013 VW Golf TDI, so it affects me), but my guess is that the fix would be updated software to apply the stricter emissions controls all the time, presumably at the expense of engine performance.

EDIT: And reducing fuel economy, which is a huge selling point of the TDI in the first place. No idea "by how much" though, and typically TDI numbers are understated, so its possible that a reduction in economy will still be in line with their claims.