David,
I don’t see any reason why they would try to ‘de-trend’ the AMO index. Moreover, to first order, I would not expect there to be any long-term trend in the AMO index. I tend to think that the AMO and PDO, and the shorter period El Nino and La Nina variability represent natural (unforced) fluctuations and oscillations that the climate system undergoes about a zero reference point – hence, no long-term trend.
It is possible that global warming might induce some change in the amplitude, frequency, or pattern of these unforced fluctuations, but I have seen no evidence that that might be happening.