Angel told the children at the club he would make sure the officers received the cards next week.
"Things like this help," he said. "It puts a smile on our faces and a tear in our eyes. I can't tell you how much this means to us."
Shanna Warren, executive director of the Boys & Girls Club, said she wanted the children, aged 8 to 12, to make the cards as a small gesture to let the officers know their work is appreciated.
Nine-year-old Riley Touris made a card decorated with a bow. One of her cousins is a police officer and she wanted to do something nice for the injured officers, she said.
"I wrote, 'I hope you get well soon,'" she said.
Green and Gutierrez were allegedly shot by Jamie Willard with his hands cuffed behind his back after the officers had loosened the restraints to make him more comfortable, Police Chief Scott LaChasse told the City Council on Tuesday.
"The individual kept complaining about the tightness of his cuffs and immobility with his arm, so there was a second set of cuffs placed on him — so he had a bit more latitude moving his arms behind him," LaChasse said.
Willard, who authorities say is homeless and from Oregon, had been arrested on suspicion of theft outside Kmart on San Fernando Boulevard on July 2.
Gutierrez, who joined the force 18 months ago, was shot several times in the chest, although the shells did not penetrate his bullet proof vest.
Green, who has served for five and a half years, had been dealing with evidence nearby when he was hit.
LaChasse praised both officers' bravery and added: "It was a real fight for life and a real will to live demonstrated by the officer who had his gun taken from him and what he was able to do was maintain custody of that gun for as long as possible."
Despite their injuries, the officers were able to restrain 30-year-old Willard, of Gresham, Ore.
His wife, Sharon Lim, 26, was also arrested at the scene and her 4-year-old daughter was placed with the Los Angeles County Department of Children and Family Services. Lim had a misdemeanor warrant for her arrest relating to theft in Orange County, authorities said.
Burbank Police released her two days later.
Willard remains in jail in lieu of $3 million bail and is due to be arraigned on July 22.