I don't follow you here. The little ice age is taken to be between about 1300 and 1800 (depending on when you count it). In the "corrected" plot they are showing temperatures higher then now during the little ice age!!!
The little ice age really started to take hold in Shakespeare's day (late 16th century) and was at its most severe around 1700.
(a) applying, as this graph does, as close to Mann et al's _unreplicable_ method as possible to the datasets actually disclosed (including updates, excluding undisclosed truncations, etc) in the Mann et al paper will
(b)actually reflect hemispheric climate history.