Images of the trio were captured on the woman's home security camera last week.
Investigators say the men showed up at the 86-year-old victim's home and said they were opening a new shop and showed her samples of vinyl.
When the woman let two of the suspects in her home, authorities say one worker distracted the woman while another man stole a briefcase of cash.
The men have now been identified as Jimmy Riley, Tommy Mack and Michael O'Hara. Authorities say the men are part of the Irish Travelers" community located in Aiken, South Carolina.
Warrants have been issued for their arrests.