And so they have. The impact of their footprints on the fragile desert site, in fact, will last "hundreds or thousands of years," according to outraged Peruvian officials.
So furious is the Peruvian government that it has barred the Greenpeace activists from leaving the country and is preparing criminal charges for "attacking archeological monuments," punishable by up to eight years in prison.
On Tuesday, culture ministry officials showed reporters aerial photographs of the damage, and said that when the Greenpeace trespassers snuck into the U.N. World Heritage site in the middle of the night, they marched single-file across the delicate volcanic rocks and white sand, leaving a path that has introduced a new line to the iconic Hummingbird-shaped figure.
The damage is "irreversible," Peruvian officials say, explaining that the rainless desert landscape is so delicate that visitors are required to obtain government permission and use special shoes to approach the site.
"What they have done is an attack on a site that is one of the most fragile in the world," cultural official Luis Jaime Castillo told reporters Tuesday.
Greenpeace issued an apology Wednesday, saying it was "deeply concerned about any offense Peruvians may have taken."
A statement on the group's Facebook page earlier in the week insisted that "absolutely NO damage was done" by the stunt, and that "no trace was left behind." The activists laid out yellow cloth lettering next to the hummingbird with the group's logo and the message: "Time for Change! The Future is Renewable."
The Greenpeace members who participated were from Germany, Argentina, Chile, Brazil, Spain and Austria, according to the group, insisting that an archeologist was on hand at the site during the episode.
The Nazca Lines are one of South America's most storied archeological wonders, a mysterious series of huge animal, human and plant symbols that were carefully etched into the ground between 1,500 and 2,000 years ago. Tourists typically view them from the air.
But by treating the sacred site like a Manhattan skyscraper, a European train terminal or some other eye-catching advertising space up north, Greenpeace seems to have trampled more than the desert.
Anger at the group from Peruvians and others on social media has been directed more at the cultural condescension of their act, and the attitude that they could barge their way into one of Peru's most sensitive places for the sake of publicity.
Of course, one of the biggest challenges for climate change activists is to convince developing countries in the southern hemisphere that they should not aspire to enjoy the same material comforts — cars, airplanes, air conditioning, et al — that have enlarged the carbon footprint of wealthier nations.
This is a delicate moral argument to make. It looks especially hollow coming from activists who are willing to break your laws and stomp all over one of your most sacred places because they think they walk on higher ground.