Sheila and Calvin Murphy said they had not received a phone call from Trump since their son, Army Spc. Etienne Murphy, 22, died in Syria in May.
"It doesn't matter if I hear from the White House or not. It's not really ... about a call or letter," Sheila Murphy told CNN anchor Alisyn Camerota, choking back tears.
"I just want people to remember my son -- Spc. Etienne Murphy -- and all the other Gold Star moms ... all those who are grieving."
The Murphys' remarks came after Trump claimed, without merit, earlier this week that his predecessors hadn't written or called the families of slain US troops, though the tradition of presidents reaching out to service members' relatives is long-established. Trump had been criticized for waiting almost two weeks
before mentioning the recent deaths of four US soldiers in an ambush in Niger.
The Murphys said they did not wish to overshadow their son's sacrifice with political jousting.
"I don't want it to be about me or about a letter," Sheila Murphy said. "I want it to be about my child and what he stood for and what they are fighting over there right now as I speak."
Murphy said that her pain was indescribable and that she had come up with a new word -- "un-get-throughable" -- to indicate what she and her family are going through. She said she and her husband had become "permanent residents in the twilight zone."
"Trust me, none of us want to be in (this) position," she said. "The worst thing I ever have been called is a Gold Star mom."
Trump also engaged in a public feud this week with a Democratic congresswoman from Florida over a condolence phone call he made to the widow of Army Sgt. La David Johnson, one of the four soldiers to die this month in Niger.
On Tuesday, Rep. Frederica Wilson said Trump had told Myeshia Johnson during the call that her husband "knew what he signed up for, but I guess it still hurt."
Wilson, who said she heard the remarks via speakerphone, called them insensitive. Trump later responded on Twitter, saying the lawmaker had fabricated the comments.
White House press secretary Sarah Sanders on Wednesday called Wilson's conduct regarding Trump's call "appalling and disgusting."