But the way she pronounces it makes a lot more sense, since the word is supposed to be derived from "itheann". It's probably a regional pronunciation.
It's formed from 'ith' + the present tense autonomous ending '-tear'. Traditionally spelt 'ithtear'. The pronunciation is /ˈitər/.
'Ithtear' is the traditional spelling, used until Irish orthography was changed in the mid-20th c.
Regularity and simplicity were sacrificed in an effort to remove 'superfluous' letters.