The company said it paid its “Oklahoma-based employees” the state minimum wage of $7.25 an hour. That money is directed to the Oklahoma Department of Corrections, which then pays the incarcerated people working in call centers, Procom said, adding that inmates can also qualify for bonus pay. But it was not immediately clear whether the prison workers received the full hourly rate of $7.25.

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A spokesman for the Oklahoma Department of Corrections did not immediately respond to a request for comment.

“In any campaign there are a whole host of services that you contract out,” said Brian Brokaw, a political consultant based in California. “So to a certain extent you have to be reliant on your point of contact — to the person that you were working with directly.”

Nowadays, he added, because mistakes are often amplified, “people are going to have to ask a few more questions than they previously had out of an abundance of caution.”

Mr. Bloomberg, a billionaire media executive and former mayor of New York City, entered the 2020 Democratic primary race in November — months after most of his rivals — and has since spent millions of dollars of his own money on political advertising and campaign operations that have helped him climb quickly to fifth place in national polling averages.

This month, he released a set of policy proposals focused on criminal justice. Among the initiatives, Mr. Bloomberg vowed to expand federal funding for alternatives to incarceration and for re-entry programs to help those released from prison find employment.

At least one other Democratic presidential candidate took notice of The Intercept’s report. Julián Castro, the former housing secretary, said on Twitter that it underscored the need for his own criminal justice plan, which would “require all prisoners to be paid a fair wage for any labor performed while incarcerated.”