Well, if Irish Troops weren't used as cannon/machine gun fodder during the Great War, that would definitely improve relations, I think.
I think you'll find that the Irish troops were never used as 'canon fodder', in as much as any other component of the Allied forces were on the Western Front. In fact, a high proportion were volunteers, the British army having a long tradition of soldiers recruited from both the north and south of Ireland (as it was then one political entity). In WWII, a quite large number of volunteers also joined the British army; unfortunately they were persecuted by the Irish goverment upon demobilisation, and this has only recently been recognised as a scandal by the present goverment.