Donald J. Trump paid his former campaign manager Corey Lewandowski $20,000 in August for “strategy consulting,” two months after Mr. Lewandowski left the team and was hired by CNN as a commentator.

The payment, revealed in Federal Election Commission filings on Tuesday, was the second monthly consulting fee paid to Mr. Lewandowski through his consulting company since he left the Trump campaign and joined CNN, raising questions about whether the network in effect has a Trump campaign strategist on its payroll.

Mr. Lewandowski still speaks with Mr. Trump regularly. Reached by phone, Mr. Lewandowski said he could not comment because of his contractual obligations with CNN.

But Steven Cheung, a spokesman for Mr. Trump, said that the payments were actually severance payments owed to Mr. Lewandowski under his old contract with Mr. Trump’s campaign.