As Carole says, English marriage certificates don't normally give the mother's name (I wouldn't say "never" but it's very unusual and I've only seen it when there's no father named).
Giving the father's name doesn't imply that he was present at the wedding, nor does it imply that he was actually still alive anywhere.
I see that Thirza is also k/a Treacy, Theresa, Teresa, and was b in Sligo.
Looking at the Notts FH CD, there are NO burials in Nottinghamshire that would fit with a William Jenkins, old enough to be Thirza's father. Nor can I see any potential matches for him in the censuses.
I'm working on the basis that William was also Irish, but Jenkins is not an Irish name so it's possible that he could have been living in Ireland when Thirza was born, rather than native to Ireland - have you looked at Army records?
