Why don't they go to Mildenhall or Lakenheath, which are military bases and not all that far away?
The range of a C-130H without aerial refueling is 2,350 miles loaded and 4,500 miles in ferry mode, but the Air Force likely wants to avoid stripping it down for ferry flights to avoid all the effort and inspections to restore it to ready mode.
The straight line distance between Thule, Greenland and Shannon, Ireland is about 2,200 miles.
The straight line distance between Thule, Greenland and Mildenhall, UK is about 2,400 miles.
The straight line distance between Thule, Greenland and Lakenheath, UK is also about 2,400 miles.
In addition, Ireland is a neutral country which makes things a lot simpler than flying into other countries.