In the letter, Weatherill says she signed off on the money in error, but doesn't say how or why.
"As CEO at the time, I take responsibility for this extraordinary event and I apologize to the people of Alberta," she said.
Lahey has said it was Weatherill's idea to send her to the Mayo.Weatherill says that's wrong, but she doesn't offer her side of the story.
Health Minister Fred Horne is seeking legal advice to determine if the province can keep the funds, Global News reports.
On Wednesday, it was revealed that Alison Tonge, another health executive, was also reimbursed $1,160 for diagnostic tests at a private Edmonton clinic in 2011.
Alberta opposition leader Danielle Smith is calling on the province to re-open the queue-jumping health inquiry in light of the expenses.
“The facts we have uncovered this week certainly warrant a much deeper look into just how widespread these instances of queue jumping actually are,” Smith said.
With files from The Canadian Press