Three U.S. governors this week asked Turks and Caicos to show mercy to Americans arrested on the islands as a Florida woman became the fifth U.S. tourist to be charged with ammunition possession. Four of the detained Americans have admitted they brought the ammunition — but by mistake. 

The governors of Pennsylvania, Virginia and Oklahoma sent a joint letter Tuesday addressed to the governor of Turks and Caicos, asking her to reconsider charges against three Americans from their states who currently face possible 12-year prison sentences — Bryan Hagerich, Tyler Wenrich and Ryan Watson.

"Like thousands of Americans each year, these individuals traveled to your beautiful territory for leisure," the governors wrote. "We humbly ask that your government—in its wisdom—temper justice with mercy and recognize that these men made mistakes but had no apparent malicious intents."

The lawmakers' plea came as the Royal Turks and Caicos Islands Police confirmed yet another American, 45-year-old Sharitta Shinise Grier of Orlando, Florida, was charged with one count of ammunition possession after two rounds were allegedly discovered in her luggage on Monday during a routine search at Howard Hamilton International Airport.

Grier, who was on her way back to Florida when she was detained, appeared in court Thursday, police said. Her next hearing is July 5.

The National Rifle Association on Thursday urged the U.S. State Department to "use every means necessary to return U.S. citizens home to America."

The State Department, which said it was aware of Grier's arrest, has warned Americans traveling to the territory to "carefully check your luggage for stray ammunition or forgotten weapons before departing from the United States," noting that "declaring a weapon in your luggage with an airline carrier does not grant permission to bring the weapon into the Turks and Caicos Islands and will result in your arrest."

Possessing either a gun or ammunition is prohibited in Turks and Caicos, but tourists were previously able to just pay a fine. That changed in February when a court order required even tourists to potentially face mandatory prison time in addition to paying a fine. It is also against TSA regulations to have ammo in a carry-on bag.

TSA confirmed to CBS News its officers missed the four rounds of hunting ammo in Watson's carry-on when he and his wife departed from Oklahoma City in April. A spokesperson for the agency told CBS News the TSA is addressing the oversight internally.

TSA Administrator David Pekoske told CBS News that U.S. screeners occasionally overlook Americans with ammunition in their carry-on luggage because screeners look at many hundreds of images during their shift rotations.

"To me, the solution here is to put more technology assists available to them," Pekosek told CBS News senior transportation correspondent Kris Van Cleave, pointing to software that would be able to identify rounds of ammunition, pieces of firearms and various knives. 

"We're never going to be able to stop everything that we want to stop," he said, recommending that travelers empty out and then re-pack their carry-on bags before heading to the airport to ensure no stray bullets tag along. 

—Kris Van Cleave and Elizabeth Campbell contributed reporting.

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• Turks and Caicos

S. Dev

S. Dev is a news editor for CBSNews.com.