Its worth noting that the paper got slightly weaker after review: the published version says
Whatever the cause of the 1age overestimate, our finding suggests that the phase relationship between CO2 and EDC temperature previously inferred for the start of the last deglaciation (lag of CO2 by 800±600 yr) seems to be overestimated.
The submitted said:
Our finding suggests that the phase relationship between CO2 and EDC temperature inferred at the start of the last deglaciation (lag of CO2 by 800±600 yr) is overestimated and that the CO2 increase could well have been in phase or slightly leading the temperature increase at EDC [my bolding]
(Note that the idiots publishing CP have moved the URLs so my old links in prev posts are broken: this should get you the submitted version).
So, the in-phase-or-leading has gone, replaced by seems-to-be-overestimated.
If you had the patience you could wade through the comments and find out why. Well its not that hard.