Wiktionary says: Munster, Aran /kɑt̪ˠ, but Cois Fharraige /kʊt̪ˠ/
Teanglann.ie sounds to me as if the Cois Fharraige (West of Galway) transcription matches the Connacht accent.
Apparently, "/ʊ/ is a near-back[ʊ] when all adjacent consonants are broad, e.g. dubh [d̪ˠʊvˠ] ('black'), and a more centralized [ʊ̟] after a slender consonant, e.g. giobal [ˈɟʊ̟bˠəl̪ˠ] ('rag')." (https://en.m.wikipedia.org/wiki/Irish_phonology#Consonants) But why is the 'a' in cat pronounced as a ʊ in the first place?!
In any case, note besides that the 't' is dental.
The definite article triggers lenition of, i.a.:
- f. ns.
- m. gs.
-> an 'h' is inserted in gs. cait