Brown's 13-year-old daughter, Ava, thought the bill looked odd, KPTV reported.
"The bill didn't look right, it was smaller, bluish tint and it just wasn't the same as the rest of the bills," Brown told the television station. Brown shared a photograph of the bill next to a legitimate one on Facebook, noting, "The troop takes the loss."
Salem police spokeswoman Lt. Debbie Aguilar said officers were able to use video surveillance to identify Ducharme, the Statesman Journal reported.
When Ducharme returned Sunday to Walmart, store loss prevention officers contacted police and he was taken into custody.
Police said they responded to one other incident in which Ducharme used counterfeit money to buy Girl Scout cookies., the Oregonian reported.
"It's not nice, it is not kind to other people and it is not fair," Ava Brown told KPTV. "Us Girl Scouts work really hard and I am proud to say I am a Girl Scout."