I compared our results at GEDMATCH (my kit is T780556), and we don't seem to have any match at all, nor do you have any with the Brennan I mentioned (kit A611991). When I lowered the segment threshold, you did have matches with two of my Mayo second cousins at (5.8 cM and 6.2 cM) which I think are large enough to indicate a connection perhaps more than 200 years or so ago.
You had a much more significant connection with one of my other matches, who has the Stenson surname. I emailed her in the past, in order to make contact, but got no response. From chromosome comparison, I know my connection to her lies in the Mayo area, but am not sure of the exact connection. I have a long segement match with her (26 cM), but the three of us share no overlapping segments, Here are the results from your comparison with her:
Comparing Kit A615946 (Mary Stenson) and A397730 (*PHL)
Minimum threshold size to be included in total = 500 SNPs
Mismatch-bunching Limit = 250 SNPs
Minimum segment cM to be included in total = 3.0 cM
Chr Start Location End Location Centimorgans (cM) SNPs
7 50,991,612 75,132,211 14.2 1,969
11 1,811,147 5,675,827 8.9 1,065
Largest segment = 14.2 cM
Total of segments > 3 cM = 23.1 cM
2 matching segments
Sorry I couldn't be of more help, but maybe you can get in touch with Mary Stenson to see whether she has helpful info about that family.