There were at least two Mary Wares see https://books.google.co.uk/books?id=VxdVAAAAcAAJ&printsec=front...
Neither of those married a John Dill.
The Sir James in Dublin was from Yorkshire and appears to have moved to Dublin in 1588. His daughter Mary died in 1620 and he built a monument in memory of her and another daughter. The only real confusion is her date of birth 1604 appears too late, but then some people have conflated her with her sister Martha.
I am disconnecting Mary Dille from parents Sir James Ware & Mary Ware (Bryden) based on your comments.
We also need to look at parents of Capt. George Dill
The Great Migration Begins has no parents for him.
Just for conversation too, you can find Sir James Ware's Funeral Entry at http://catalogue.nli.ie/Record/vtls000529291#page/173/mode/1up if you want to know who was there!
You can't tell whether any of the women attended the funeral, though Mary's funeral certificate suggest no http://catalogue.nli.ie/Record/vtls000529284#page/188/mode/1up
As for John Dill he isn't mentioned nor is Emanuel Downing who was married to Ann who is also dead http://catalogue.nli.ie/Record/vtls000529284#page/217/mode/1up. The Downing children are all supposed to have emigrated to Massachusetts.
There is a different version of the truth at http://catalogue.nli.ie/Record/vtls000529291#page/123/mode/1up
This version omits Russel and marries Ann to Humphrey Reynolds which is clearly wrong as per Ann's funeral entry and Humphrey's will https://www.familysearch.org/ark:/61903/3:1:3QS7-99L4-FQ1T?cat=224404
Mary is still the wife of Christopher Conway though.