"We suggest parents have a chat with the grandparents about the parameters they have set for their kids online, whether they want Fortnite being played in the lounge room rather than the bedroom, how much time they want them spending on it, and maybe even taking the grandparents through what devices they're using," Inman Grant told News Corp.
"We know kids can subvert and be pretty sneaky. Granddad might be thinking he's effectively been the cyber policeman when he takes away the iPad, but when the kid pulls out his iPhone we want him to be wise to the fact that the grandkid is continuing the gaming."
Complicating the issue somewhat is the one thing most kids generally know and love about time spent at grandma and grandpa's: it's a little bit different in lots of ways, and often not as strict.
"We also know grandparents love to spoil their grandkids but that doesn't mean they need to be permissive – or lack knowledge – when it comes to online safety," Inman Grant said.
According to eSafety Commission research, about a quarter of people aged 50-69 have low to no digital literacy, and that percentage increases to more than half for the over-70s.
Those stark findings have prompted a new how-to guide that will equip even non-tech-savvy grandparents with tools to help them deal with issues that may come up when kids are in their care.
"We're trying to make technology more accessible," Inman Grant said. "[Grandparents] might not know what cyber bullying is or online grooming is ... but this will give them some of the grounding and tips as to how to ask their grandkids questions that seem relevant."
Helen Anderson, grandmother to Isamu, 7, and Kiera, nearly 5, said she was "very bad" with technology herself, but the eSafety Commission work had helped her realise some of the dangers lurking on the net for kids.
With Isamu long since proficient at turning on a computer, Anderson said she asked her son to install security software on her home PC, as well as a timer so games of Minecraft did not go on forever.
Asked if her grandchildren had ever seen anything online that upset or confused them, Anderson said she wasn't aware of any such incidents, but she knew how easy it was for damaging material to flash up on screen.
"I'm very aware that you can get the wrong thing when you're looking for something else," she said. "You put a word in and it comes up something totally inappropriate."