Bush, the 41st US president, is also referred to as "Bush 41", "Bush the Elder" and "Bush Senior" to distinguish him from his eldest son, George W. Bush, who became the 43rd US president.
“Thousand Points of Light. I never quite got that one. What the hell is that? Has anyone ever figured that one out?” Trump said during a free-wheeling campaign rally Thursday in Montana.
Bush, 94, used the slogan to name a private organization he had established to promote volunteerism, Presstv Reported.
Trump, however, said it was no match for his slogans, “Make America Great Again” and “Putting America First.”
The jab at the Bush prompted negative reactions, with many jumping to the senior Bush’s defense.
Ari Fleischer, who served as press secretary for Bush’s son, former President George W. Bush, said what Trump did was “rude.”
"Going after a 94-year-old, former President's promotion of volunteerism. I don't mind POTUS being a fighter. I do mind him being rude," he wrote on Twitter.
Richard Haass, who served as Bush’s special aide and as a senior director on his National Security Council, sammed Trump’s “offensive” move.
Jon Meacham, who penned a biography about Bush, and Reverend Jesse Jackson Sr., who ran as a Democratic presidential candidate the year that Bush was elected president, also defended the former head of state.
The Bush family has been reluctant in defending Trump in the wake of heavy attacks by Democrats.
Some observers attribute the divide to Trump’s damaging presidential campaign, which saw him eliminate H.W.Bush’s other son, former Florida Governor Jeb Bush, in a battle that often became personal.
Trump chose to skip the funeral of H.W. Bush’s wife and former first lady, Barbara Bush, in April.
Bush served as US president from 1989 to 1993, and was vice president from 1981 to 1989 during the 8-year administration of former President Ronald Reagan.
Bush has suffered from poor health in recent years. In January, he spent 16 days at the same hospital in Houston being treated for pneumonia. During that time, he was on a ventilator and was in ICU.