Some of this may have already been posted elsewhere.
1937 Rose Dorothy Gillick, single, born 24 Sept.1886 South Australia arrived in U.S. from Japan via Canada. Address was 2220 Park Ave., N.Y.C. (there in 1940 U.S. Census).
Naturalization record (petition 1936) shows her as a 'graduate nurse' so she might have been working at Stamford Hospital (probably about 15 walk from Clinton Ave.).
Therefore, she can't be the Mrs. Rose Gillick from newspaper articles or the Rose Gillick whose mother died in Cavan in 1944.
I can't see a Rose Gillick death in Connecicut.
With an Irish ancestry she may well have had some contact with a "Cavan Society" which is another clue for us in our search for the Irish connection.
I've already said several times that this is a Mrs. Rose Gillick whose mother was in Ireland.