Hello sancti,
I think there's an incorrect spelling floating around. Mc Inruie doesn't appear in Griffiths Valuations (on John Hayes failteromhat.com website) although maybe maybe the family wasn't in Ireland at that time.
I tried McInr ... and found the following in Co. Clare.
Michael Mc Inrehy, Kilconnell, Kilmacrehy. Clare
John Mc Inreney, Binvoran, Kilmurry. Clare
Michael Mc Inreney, Binvoran, Kilmurry. Clare
There's also a long list of people named Mc Inroe. If you could find out if other families from Co. Clare attended St Patricks that would help.
Christopher