The TTF has written to the director of "I Bought a Rainforest", which aired in June, to highlight that the suggestion was not backed by UK trade statistics.
"In 2013, our trade statistics show that there was 39m3 of tropical hardwoods including the description of ‘mahogany’ (not all of which will be mahogany) imported from Peru," outgoing chief executive John White said in his letter.
"In the first quarter of 2014, nothing was imported from Peru and the only volume of tropical hardwoods including the description ‘Mahogany’ imported from the region was 34m3 from Brazil and 512m3 from Honduras."
Mr White said the programme made some "excellent points" about the difficulty of trading in the region but the TTF did not want it to misrepresent the timber sector, "whose trade in legal products brings income to the people whose livelihoods depend on these forests".
The programme followed wildlife photographer Charlie Hamilton James, who bought 100 acres of Peruvian rainforest.
