I'm going to put my Floirin's worth. Yes, Mise, le Meas means Respectfully Yours.
As Thompson notes, the Irish alphabet can be a bit of a minefield, as well as pronunciations. For example, for many Irish people, to this day, it is impossible to get your tongue around the 'Th" sound, Hence the 'DIS, DAT, DESE, DOSE' way of speech. In modern Irish pring, having an 'h' is a substitute for the old dot, or buailte sign over letters, signifying they were to be aspirated. For example M( buailte) is now mh and is pronounced as a soft v or even silent, depending on the Munster, Connacht or other dialect.
Mather ( mother) is pronounced MawHer. Note the T is silent, so no th sound.
but Mo Mhather (My Mother) is pronounced Muh WawHer
70 years old, in Australia for 45 years and still remember the odd scraps!