A good samaritan on Reddit shared with me a link to the story by none other than HH Munro (Saki). It is a short story titled "The Background".
Signor Pincini was, perhaps, the most brilliant master of tattoo craft that Italy had ever known, but his circumstances were decidedly impoverished, and for the sum of six hundred francs he gladly undertook to cover his client's back, from the collar-bone down to the waist-line, with a glowing representation of the Fall of Icarus. [...]
But he bore on his back the burden of the dead man's genius. On presenting himself one day in the steaming corridor of a vapour bath, he was at once hustled back into his clothes by the proprietor, who was a North Italian, and who emphatically refused to allow the celebrated Fall of Icarus to be publicly on view without the permission of the municipality of Bergamo. Public interest and official vigilance increased as the matter became more widely known, and Deplis was unable to take a simple dip in the sea or river on the hottest afternoon unless clothed up to the collar-bone in a substantial bathing garment. Later on the authorities of Bergamo conceived the idea that salt water might be injurious to the masterpiece, and a perpetual injunction was obtained which debarred the muchly harassed commercial traveller from sea bathing under any circumstances. Altogether, he was fervently thankful when his firm of employers found him a new range of activities in the neighbourhood of Bordeaux. His thankfulness, however, ceased abruptly at the Franco-Italian frontier. An imposing array of official force barred his departure, and he was sternly reminded of the stringent law which forbids the exportation of Italian works of art.
[...] And then one day, at an anarchist congress at Genoa, a fellow-worker, in the heat of debate, broke a phial full of corrosive liquid over his back. The red shirt that he was wearing mitigated the effects, but the Icarus was ruined beyond recognition. His assailant was severely reprimanded for assaulting a fellow-anarchist and received seven years imprisonment for defacing a national art treasure.