Carl and Marsha Mueller have endured the anguish of losing their daughter after the aid worker was taken hostage by ISIS in Syria in 2013 and then received confirmation of her death at age 26 in 2013 following 18 brutal months in captivity.
President Trump announced Sunday that al-Baghdadi, who had repeatedly raped Mueller during her time in captivity, had been killed a day earlier in a U.S.-led raid in northwestern Syria.
"In that moment, it's kind of hard to explain, there's so many emotions," Carl Mueller told Savannah Guthrie in an exclusive interview on TODAY Wednesday.
"I'm glad that evil person is gone... if you were a parent, and this man did what he did to Kayla to your child and they got him out, how would you feel? The parents, I think they could answer that question without me saying too much more."
Trump paid tribute to Mueller during his press conference about the raid, saying she was "a beautiful woman" who was in Syria "to help people." He also spent 18 minutes on the phone with Carl and Marsha offering his condolences and answering their questions, the couple said.
"I was able to tell him our 1% chance that Kayla's still alive and why we feel that 1% chance is still there," Carl explained. "And he said, 'I hadn't heard that. I'll look into that Monday.'"
The mission that claimed al-Baghdadi's life was also named in honor of their daughter.
"We cried,'' Marsha Mueller said. "It was just an amazing gift for Kayla. I know Kayla, Kayla would say this is for all of us, this is for all the hostages and all the people over there that have suffered so much through this group. Kayla would want it to be for everyone, all the people that she was with."
The couple are now holding out hope that her remains, which have never been found, can be brought home. ISIS claimed in February 2015 that the Arizona native died in a coalition airstrike in Syria. U.S. government officials confirmed that she had died but did not confirm her cause of death or when she died.
Mueller's parents still have a bit of hope that their daughter could still be out there.
"Ninety-nine percent of that is my hope is Kayla truly is with her Lord and Savior. I know God was with Kayla every step of the way," Marsha said. "I could tell that from her letters... He came through at such wonderful times for us when we were just losing hope.
"But something always would happen. We did get three photos, but Kayla was completely covered. All you see is this part of her face. She does have a gash in her cheek, and it's horrific to look at them. She looks lifeless to me."
She continued, "But then we started getting these messages that people said she wasn't gone and don't be surprised if ISIS did this. The truth wasn't always told to us, so we just decided it was our mission, and especially me, and people thought I was crazy.
"Until she's home, we've got to find her. We've got to find truly what did happen to her because we do not know, and we've got to get her back home here. That's what's important."
Kayla's father explained he and his wife learned a lot about how the U.S. government handles these situations and said, "They never take one piece of intel and act on it. They have to have at least two, maybe three, before it's actionable. And they never take intel from a terrorist group as factual.
"So, the only thing they based Kayla's death on was: One, ISIS said she was dead. We got the email. Two, the three photographs. That's it, and we've had those photographs looked at by other people. They're not so sure. And they would make the hostages do those photos, the death photos."
Kayla had dedicated her life to humanitarian work, volunteering with aid organizations in India, Israel and the Palestinian territories before deciding in 2012 to work with refugees at the Turkish-Syrian border. She was taken captive in 2013 in Aleppo, Syria, after leaving a Doctors Without Borders Hospital.
"I want people to see the light in Kayla in such utter darkness, how she just said there is always light,'' Marsha said. "And I also want people to see that she even told people that as far as where she was, maybe she was supposed to be there, this is where she was supposed to be all along. She always wanted to help."
At the end of the interview when Savannah thanked the couple for sharing Kayla's story, Marsha said, "Thank you. Kayla should be here, and we're going to find her."