A man has been arrested over the theft from TD Olivia Mitchell on the Luas.
The TD had her purse, containing €250 and credit cards, stolen on Monday at 5.30pm on the green line, and the man was tracked down after gardai went through CCTV footage.
It is believed that he is a member of a gang of three that has been operating on the Luas in recent weeks.
"It was a nuisance and an inconvenience but it's great they got them from the CCTV footage that they had to sift through," Ms Mitchell told the Herald.
There were 90 thefts on the Luas in 2013 and undercover gardai are patrolling both Luas lines as the crime problem on the capital's tram system continues. At least two arrests relating to Luas thefts have been made so far this year.
Pearse Street Garda Station dealt with two incidents that occurred on the green line between Harcourt St and St Stephen's Green Luas stops.
Transdev, which operates the Luas, revealed to the Herald that 90 thefts were reported in 2013 but that figures for previous years are not available yet as they are "focusing on services and the weather" this week.
The National Transport Authority, when contacted by the paper, said it was a matter for Transdev, and the gardai said that while they cannot comment on individual cases they fully investigate every crime reported on the Luas.
As gardai from Dundrum investigate the crime and its links to other similar thefts over the past week, the Herald has learned that "regular undercover patrols" are being mounted on the Luas Red Line.
The undercover patrols on the red line are being co-ordinated by officers based at Store Street Garda Station.
"We have plain clothes and uniformed gardai on the Luas on a regular basis. Gardai also patrol the Luas stops particularly at busy times in the morning and the evening," a senior source said. "These patrols are part of Operation Spire, the gardai's attempt to clean up anti-social behaviour problems on O'Connell Street and the areas around it."
In the last week of January, 304 suspect searches took place with 42 detections for possession or supply of drugs and 99 behavioural warnings issued as part of Operation Spire.
The senior source also revealed that gardai get great co-operation from Transdev, the company that operates the Luas.
"Whenever we require CCTV we get it in a very prompt and efficient fashion and it is often of very good quality," he explained.
An investigation by the Herald has established the Luas tram service was plagued by anti-social behaviour during 2013.
Almost 1,000 incidents of anti-social behaviour and threats to passengers and staff occurred on the Luas last year.
But the operators of the tram system have refused to reveal how many thefts there were in 2013.
Transdev only said that it was "accurate to say the majority of incidents were on the Luas red line".
In 2013 there were 677 public order offences, and a number of prosecutions are currently with the gardai.
Staff and passengers were also subjected to abusive behaviour on 199 occasions.
In 2012 there were 250 incidences of abuse, including members of the public receiving "serious verbal threats" and inspectors being spat on.
Despite the figures, Transdev said that "the Luas red and green line services were safe, reliable and frequent".
But the operator would not reveal how many thefts had occurred on the system, nor could it say which line the incidents of anti-social behaviour had happened on.
Transdev said that it would continue to work with the authorities to combat crime.