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(CNN) —  

On the day that President Donald Trump announced the death of Abu Bakr al-Baghdadi, the parents of Kayla Mueller, who was kidnapped and reportedly raped by the ISIS leader, say they are feeling a “roller coaster of emotions.”

“Well, it’s a roller coaster of emotions whenever this ugly situation raises its head, but it’s become part of our life over the last five and a half years,” Kayla’s father Carl Mueller told CNN in a phone interview Sunday afternoon.

In 2012, Kayla traveled to the Turkey/Syria border to work with the Danish Refugee Council and the humanitarian organization Support to Life, which assisted families forced to flee their homes. She was taken hostage by ISIS in Aleppo, Syria, in 2013 after she visited a Spanish MSF (Doctors Without Borders) hospital. The family confirmed Kayla’s death in 2015 but her body has not been recovered.

Carl and Marsha Mueller said they were at home in Prescott, Arizona, on Saturday when they were messaged by a reporter about the possibility that Baghdadi may have been killed. Marsha said her first reaction to the news was uncertainty, because of the previous times the ISIS leader was believed to have been killed.

The Muellers received the official confirmation of Baghdadi’s death in listening to Trump’s news conference Sunday morning. They praised and thanked the President, the US military and special forces for taking action.

“We were deeply touched by what he said. We were grateful that they didn’t mess around and went right in,” Marsha Mueller said in a phone interview.

White House national security adviser Robert O’Brien said the US military operation that resulted in the death of Baghdadi was named after Kayla Mueller.

In an interview with NBC’s “Meet the Press” on Sunday, O’Brien said, “The chairman of the joint chiefs of staff named the operation that took down al-Baghdadi after Kayla Mueller, after what she had suffered,” adding “that was something that people should know.”

In speaking about Kayla’s life and the US operation against Baghdadi, Mueller’s mom says she still has hope.

“I just want to say how grateful we are to this administration, to the military, and to the special forces that went in,” Marsha Mueller said. “My hope is that this will help us get answers to what really happened to Kayla and get her home.”

Her family wants Kayla to be remembered as someone with a “tender heart” and “her gift to always have time to help people.”

“Kayla always had a heart to help people. All people,” Marsha Mueller said. “It didn’t matter if they didn’t think exactly like you or if they thought differently. She had a gift of meeting people where they were and trying to learn from them so she could better understand their side.”

CNN’s Mike Callahan and Ralph Ellis contributed to this report.