Juan Luis Garcia wrote an open letter to Lee asking for help getting compensation for the designs he said he created for the agency, the name of which wasn't reported, The Hollywood Reporter said Friday.
Garcia said he spent nearly two months on the project but when the agency gave him a low bid on his work, he declined.
He said the agency used his work anyway without paying him.
"I couldn't believe that you had been using and claiming copyright on three of those very same posters I designed," Garcia wrote to Lee. "I just couldn't believe it. I perceive you as an advocate of the arts and artists and have a sinking feeling that you are as much of a victim in this as I am."
Lee responded to Garcia's letter on Twitter Thursday, saying: "I Never Heard Of This Guy Juan Luis Garcia,If He Has A Beef It's Not With Me.I Did Not Hire Him,Do Not Know Him.Cheap Trick Writing To Me.YO."
One fan wrote on Lee's Instagram page asking the director to help Garcia.
"Why Should I Pay Someone Who I Never Met Nor Had Any Contact With Ever? He Never Made Any Deal With Me.Why Don't You Pay Me For Your Stupid Text On Thanksgiving Day?" Lee responded.
Garcia said he will take legal action against the agency if necessary.