The fund was less than $700 from its $5,000 goal late Monday afternoon.
Because of his love of cats, Moore's family is also directing those who wish to donate in Parker's name to a charity called Good Mews, according to restaurant owner Martin Kohnen.
The restaurant is also planning a series of benefits in which a portion of the revenue will be donated to those funds as well as for another employee who police said was shot in the head during the holdup.
The injured worker, identified as a 21-year-old Jordan Christian of Centerville, is recovering at home after being released from the hospital last week. He could not be reached for comment.
Details of the benefits have not been finalized, Kohnen said.
"We loved Parker. .. He was a friend of ours," Kohnen said Monday. "He wasn't just a co-worker. He meant something on a personal level to everyone, and we're all heartbroken for his family. We just want to wish them whatever comfort we can through this time."
The restaurant reopened Friday for the first time since the slaying. Employees and customers gathered the previous night to remember Moore before reopening.
A makeshift memorial of flowers, candles, a card and photos of Moore rest at one end of the bar.
"We're a restaurant, so all we know how to do is prepare and serve food, and so everybody wanted to get back to doing that, .. and that's helping us cope with our grief," Kohnen said. "It's been nice to have a sense of routine ... and a sense of purpose in the restaurant in order to just help with the grief. It's very difficult."
Moore, a shift leader at the restaurant, wasn't scheduled to work the night he was shot, according to his family's GoFundMe post. But a friend had called and asked him to fill in.
Moore had picked up his car from the repair shop earlier that day, and he'd nailed an interview for a new job that he was scheduled to start in just over a week, the post said.
"We are broken, and we miss Parker — today, tomorrow, and forever," his family said in the post. "Parker loved his family, friends, customers, animals — especially cats, the lake, soccer, hiking, music, photography, the color purple, history, video games, and being outdoors.
"We want his light to shine on — to help others reach their goals and dreams. We started this scholarship fund in Parker’s name to do that. We miss him so much, and we know that he would have loved having his name on something like this. 100 percent of all donations gathered here will go to others. Nothing will be kept by his family.
A service to honor and celebrate Moore's life was held Sunday in Anderson, South Carolina, where his father, Andrew Eric "Andy" Moore and his wife, Misty Anderson Moore, live. Parker Moore had lived in Kathleen with his mother, Leah Heaton Maas and her husband, Chris Maas.
"His friends said it best, 'Parker was a beautiful soul with the purest, most gentle heart. He was one of those fires that burned brighter than the rest,' " his family said in the post.
His father, Andy Moore, told the Independent Mail in Anderson that Parker Moore may have saved the life of a coworker by pushing him out harm's way, with the bullet grazing him.
"I wouldn't expect anything less of him," Moore told the newspaper. "I'm so proud of him. That's a little comforting to me."