Fallen branches, leaves, and trees not already needed for any animal habitats or nutrition. The string to hold it together is, of course, woven from your own hair.
Also, no fires, since burning wood releases carbon into the atmosphere, so warmth can only be generated by sewing together carcasses of animals who died natural deaths.
And finally, following a strict diet to minimize gastro-intestinal discomfort lest you release methane into the atmosphere.
Or just make a rope from your own hair and hang yourself with it, as that's honestly the only way you can make no impact on the environment. I mean, don't do this, obviously, but that's it. As long as we exist, we affect the environment, so we should just do what we can to mitigate the negative effects. The perfect is the the enemy of the good.