The four tweens sat on a bench at the veterans memorial in Eden Prairie, shielding their cellphones from the glare of the midday sun. They exchanged notes about their latest Pokémon Go captures. As they hunched over their phones, their feet dangled above an inscribed quote: “Eternal vigilance is the price of liberty.”

Purgatory Creek Park has seen a boom of these vigilant visitors recently, said Jay Lotthammer, the city’s parks and recreation director. He just wishes that attentiveness extended beyond a handheld screen.

He’s sent requests to Niantic — the company behind Pokémon Go, the popular app and augmented reality game — asking them to disperse the handful of Pokestops around the park away from the veterans memorial.

The hundreds of people who come “at all hours of the day and night” have been crowding around the memorial, tromping through flower beds and wandering, eyes down, through the space intended for quiet reflection.

“From what we’ve heard, this is one of the most desirable spots for the game in the state,” Lotthammer said. “As long as the Pokémon are here, the people will come. Of course we want people in our parks — that’s great for us — but it’s got to be tweaked and dispersed a little.”

Over the lunch hour on Friday, the park’s parking lot was full. More than 150 people were gathered with their phones, walking around in work attire or sprawled out on picnic blankets, collecting the animated characters.

Jim Beck, 46, leaned up against a bronze sculpture of a battlefield cross — a rifle rising above a pair of combat boots with a helmet placed on top.

“I just think it’s a double standard,” he said, keeping his eyes on his phone and the Magikarp he was trying to capture. “The city wants people out and active but then want to take away the thing that’s bringing us out and off the couch. I would never have come to the memorial if it wasn’t for this game.”

The director of Fort Snelling National Cemetery, John Knapp, agrees with Lotthammer and has adopted a recently issued nationwide policy banning gaming in the country’s national cemeteries. Over the past few days, he’s also sent requests to Niantic, asking for the removal of 16 Pokestops in the cemetery. So far, three have been removed and he’s personally asked several Pokémon hunters to take their game elsewhere.

“These are hallowed grounds,” he said. “We want it to be a space of decorum.”

Twelve-year-old Ryan Kelly said he thinks Eden Prairie’s memorial should be offered the same respect, but he understands the appeal of trying to “catch ’em all.”

After capturing “a lot” of Pokémon around the memorial, he took a moment to walk around with his father and look up at the bronze ­sculpture of fallen soldier slung over the shoulders of a comrade.

“I definitely tried to look around and think about it,” he said. “That’s important. But I can’t say it was the reason I came out here.”

Mara Klecker • 612-673-4753