And in theory it shouldn't be difficult, since the miscreant - reportedly an artist named Casey Nocket, over from New York on a tour of western US beauty spots - posted her work on Instagram, for all to see.
Her account on the photo-sharing website has been deleted, but not before various media outlets including the San Francisco Chronicle got hold of it, publishing exchanges in which she shamelessly defends her work.
"It's art, not vandalism. I am an artist," she wrote, cited by the Denver Post.
In all, she reportedly left her mark in 10 national parks, including Rocky Mountain National Park in Colorado.
The case has already drawn over 10 000 signatures on a White House "We the People" petition, which calls for authorities to "pursue the most serious of charges for these offenses."
"Casey Nocket has traveled around the western US vandalizing National Parks and National Monuments with her 'art.'
"She has acknowledged that she is not in the right only in regards to her use of acrylic paints, she responded to a question about her paint materials on Instagram with the comment 'I know, I'm a bad person'," the petition states.
The National Park Service said: "While we can't discuss details of a case under investigation, we take the issue of vandalism seriously."
It added: "There are forums for artistic expression in national parks because national parks inspire artistic creativity. These images are outside that forum and outside the law.
"National parks exist to preserve and protect our nation's natural, cultural and historic heritage for both current and future generations. Vandalism is a violation of the law and it also damages and sometimes destroys often irreplaceable treasures that belong to all Americans."
The parks service highlighted the case in a statement last week.
Apart from the petition, people have also been airing their disgust on Twitter:
CASEY NOCKET BETTER KNOCK IT THE FUCK OFF pic.twitter.com/u6YwjYy5hN— ? supernova girl ? (@bumblesweet) October 23, 2014
What do you think about this case? Is it vandalism or is she adding to the landscape? Tell us in the comment section below.