On the night of March 5-6, 1854, at 1 AM to 2 AM, several men descended upon the grounds to steal the Pope’s Stone. What happened next was vividly described in the March 8, 1854 Daily National Intelligencer on page 1. The night watchman George Hilton was on duty in his watch box, so the men tied clothes-line cords around the box, and warned him to be quiet. The thieves also pasted newspapers over the box windows facing the lapidarium. Somehow they got the block into a handcart used by the workmen, and carried it off for dumping in the Potomac River.
This wasn’t as far a trip as it would be today. Back then, the Potomac was much wider than it is now, before the land reclamation of the 1870s and 1880s, and it flowed quite close to the southwest corner of the Monument.
Afterwards, the watchman came under suspicion. After all, he did have a double-barreled gun, and the pasted-over windows could be raised or lowered at will. He was fired from his job.
On March 9, 1854, on page 1, the Intelligencer announced that the Washington National Monument Society, in charge of the project, had put up a $100.00 reward for catching the thieves, raised on April 4 to $500.00. The crooks were never caught, however.
In addition to stealing the Papal donation, however, the Know-Nothings also took over control of the Washington National Monument Society, and as this other website notes, that's when the progress on the monument slowed down, because the Know-Nothings wanted to make sure that there was no Catholic or foreign influence on the project:
They then took over the Society for several years, did some shoddy construction work which later had to be removed, and presided over the drying up of funding for the project. By attempting to turn the monument of all people in honor of Washington into a monument to themselves, they found themselves suddenly confronted with a Tower of Babel that was impossible for them to finish.
The Know-Nothings as a party were a short-lived phenomenon, even if anti-Catholicism never entirely died out. They quickly fell apart over the issue of slavery, with Northern members supporting abolition and Southern members opposing it. They eventually relinquished control of the Society, which in any case by 1860 was depleted of funds thanks to public dissatisfaction with the Know-Nothings running the show. After the interruption of the Civil War, thanks to the efforts of President Ulysses S. Grant and a government takeover of the project, the Washington Monument was eventually completed and dedicated in 1884.
As Kevin Schmeising noted in his segment, Father James E. Grant (any relation to Ulysses?) donated a replacement stone in 1982 inscribed in Latin "A Roma Americae". You may see a picture of it here from the National Park Service.
As The Blog of the Courtier notes, however, the Know Nothings were certainly ignorant of George Washington's friendly tolerance of Catholics. He ordered his soldiers not to observe the Fifth of November/Pope Day/Guy Fawkes Day because it would offend the Catholic French and Polish officers assisting the Continental Army in the War for Independence. And he wrote to some Catholics when they congratulated him on his election as the first President of the United States words that would shock the Know Nothings:
As ever, hatred and prejudice make us stupid.