Currently, he said, the company is designing a separate E.P.A. challenge coin to be given to emergency workers who responded to last year’s hurricanes and wildfires. The coin, Mr. Perez said, is similar to one the company designed for a division of the E.P.A. a few years ago that depicted emergency responders on one side and the agency symbol and division name on the other.
The main design of the current E.P.A. challenge coin was conceived under President Barack Obama’s first administrator, Lisa P. Jackson. One side bears the agency seal with her signature underneath and her name stamped along the rim. The other side has an image of outstretched hands holding up the earth.
The cost of the coins ranges roughly from $3 to $6 apiece (not including the molds) depending on size, thickness, design and number of coins produced, according to Mary Harms, the owner of Challenge Design, a company that makes challenge coins for the White House Military Office.
Mr. Slotkin, along with one of the people familiar with the initial discussions and who requested anonymity, said Mr. Pruitt wanted his coin to be about twice as large as the current one while featuring images of more personal relevance, such as the buffalo. Mr. Slotkin said that, when he asked Mr. Pruitt’s aides, why put a buffalo on the coin, they answered, “But he’s from Oklahoma.”
“At one point he wanted a bible verse, but staff talked him out of it,” Mr. Slotkin said. He said he did not recall which verse had been considered.
Asked about the details of the E.P.A.’s coin redesign, Mr. Wilcox, the E.P.A. spokesman, said in a statement: “Administrator Pruitt does not have a challenge coin.”
Other agencies have made changes to their own challenge coins. Ryan Zinke, the interior secretary, issued coins last year that display the United States seal on one side and his agency’s logo, a buffalo on a prairie with mountains and a rising sun, on the other. Mr. Zinke’s name is stamped around the rim. Earlier Interior Department challenge coins did not bear the secretary’s name.
Mr. Trump also has remade the presidential challenge coins, substituting his campaign slogan, “Make America Great Again,” for the national motto, e pluribus unum.