Bhagavad Gita, Chapter 4, Verse 14

Actions do not taint Me, nor have I any thirst for the result of action. He who knows Me thus is not fettered by action.

Acting without craving the outcome is what actually keeps a person from getting weighed down by it.

Krishna offers himself here as the working example. Action alone was never the problem, wanting something personal out of it was, and staying free of that wanting is what keeps the same action from leaving a mark.